Find the Diameter of the Circle If the Length of a Chord is 3.2 Cm and Itd Distance from the Centre is 1.2 Cm - Mathematics

Advertisements
Advertisements
Sum

Find the diameter of the circle if the length of a chord is 3.2 cm and itd distance from the centre is 1.2 cm.

Advertisements

Solution

AD = DB = 1.6 cm (Perpendicular from centre to a chord bisects the chord)

In right Δ ODA ,

By Pythagoras theorem , OA2 = OD2 + AD2

= 1.62 + 1.22

= 2.56 + 1.44

OA2 = 4

OA = 2 cm

Diameter (AP) = 2 (OA) = 2 (1) = 4 cm

  Is there an error in this question or solution?
Chapter 17: Circles - Exercise 17.1

APPEARS IN

Frank ICSE Class 10 Mathematics Part 2
Chapter 17 Circles
Exercise 17.1 | Q 12

RELATED QUESTIONS

A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in em) is

`(A) 5sqrt 2`

`(B) 10 sqrt2`

`(C)5/sqrt2`

`(D) 10sqrt 3`


Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.


ABCD is a quadrilateral such that ∠D = 90°. A circle (O, r) touches the sides AB, BC, CD and DA at P,Q,R and If BC = 38 cm, CD = 25 cm and BP = 27 cm, find r.


In fig., circles C(O, r) and C(O’, r/2) touch internally at a point A and AB is a chord of the circle C (O, r) intersecting C(O’, r/2) at C, Prove that AC = CB.


Fill in the blanks:

An arc is a __________ when its ends are the ends of a diameter.


If the tangent at point P to the circle with center O cuts a line through O at Q such that PQ= 24cm and OQ = 25 cm. Find the radius of circle


In the given figure, BC is a tangent to the circle with centre O. OE bisects AP. Prove that ΔAEO~Δ ABC.


Prove that two different circles cannot intersect each other at more than two points.


In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC
at P and OA at Q. Prove that:
(i) ΔOPA ≅ ΔOQC, (ii) ΔBPC ≅ ΔBQA.


In the given figure, if arc AB = arc CD, then prove that the quadrilateral ABCD is an isosceles– trapezium (O is the centre of the circle).


In the given figure ABC is an isosceles triangle and O is the centre of its circumcircle. Prove that AP bisects angle BPC .


In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight sided polygon inscribed in the circle with centre O. Calculate the sizes of:
(i) ∠AOB,  (ii) ∠ACB  (iii) ∠ABC


Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle.


In the given figure, the chord AB of the larger of the two concentric circles, with center O, touches the smaller circle at C. Prove that AC = CB.


Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.


A quadrilateral is drawn to circumscribe a circle. Prove that the sums of opposite sides are equal ?


In Fig 2, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of ΔEDF (in cm) is:


Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15 cm, then find the length of BP.


A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC ?


The perimeter (in cm) of a square circumscribing a circle of radius a cm, is


In the given figure, ABCD is a cyclic quadrilateral. If ∠BCD = 100° and ∠ABD = 70°, find ∠ADB.


On a semi-circle with AB as diameter, a point C is taken, so that m (∠CAB) = 30°. Find m(∠ACB) and m (∠ABC).


AB and CD are common tangents to two circles of equal radii. Prove that AB = CD.


In the given figure, PO \[\perp\]  QO. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OTare right bisector of each other.


Choose correct alternative answer and fill in the blank. 

Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is .........


Radius of a circle is 10 cm and distance of a chord from the centre is 6 cm. Hence the length of the chord is ______.


The point of concurrence of all angle bisectors of a triangle is called the ______.


The circle which passes through all the vertices of a triangle is called ______.


Length of a chord of a circle is 24 cm. If distance of the chord from the centre is 5 cm, then the radius of that circle is ______.


The length of the longest chord of the circle with radius 2.9 cm is ______.


Radius of a circle with centre O is 4 cm. If l(OP) = 4.2 cm, say where point P will lie.


The lengths of parallel chords which are on opposite sides of the centre of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is ______.


Find the length of the chord of a circle in the following when: 

Radius is 6.5 cm and the distance from the centre is 2.5 cm 


AB and CD are two equal chords of a drde intersecting at Pas shown in fig. P is joined to O , the centre of the cirde. Prove that OP bisects  ∠ CPB. 


In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –
(1) m(arc PR)
(2) m(arc QS)
(3) m(arc QSR)  


In the given figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof. 


In the given figure, seg MN is a chord of a circle with centre O. MN = 25, L is a point on chord MN such that ML = 9 and d(O,L) = 5. Find the radius of the circle. 


The figure given below shows a circle with center O in which diameter AB bisects the chord CD at point E. If CE = ED = 8 cm and EB = 4 cm,
find the radius of the circle.


In the following figure, OABC is a square. A circle is drawn with O as centre which meets OC at P and OA at Q.
Prove that:
( i ) ΔOPA ≅ ΔOQC 
( ii ) ΔBPC ≅ ΔBQA


Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points?


Suppose you are given a circle. Describe a method by which you can find the center of this circle.


In the given circle with diameter AB, find the value of x.


In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.


If O is the centre of the circle, find the value of x in each of the following figures


ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.


Use the figure given below to fill in the blank:

R is the _______ of the circle.


Use the figure given below to fill in the blank:

______ is a chord of the circle.


Use the figure given below to fill in the blank:

If the length of RS is 5 cm, the length of PQ = _______


Use the figure given below to fill in the blank:

If PQ is 8 cm long, the length of RS = ________


Construct a triangle ABC with AB = 4.2 cm, BC = 6 cm and AC = 5cm. Construct the circumcircle of the triangle drawn.


Construct a triangle PQR with QR = 5.5 cm, ∠Q = 60° and angle R = 45°. Construct the circumcircle cif the triangle PQR.


Construct a triangle PQR in which, PQ = QR = RP = 5.7 cm. Draw the incircle of the triangle and measure its radius.


The diameter of a circle is 12.6 cm. State, the length of its radius.


Draw a circle of diameter 7 cm. Draw two radii of this circle such that the angle between these radii is 90°. Shade the minor sector obtained. Write a special name for this sector.


State, if the following statement is true or false:

If the end points A and B of the line segment lie on the circumference of a circle, AB is a diameter.


If the radius of a circle is 5 cm, what will its diameter be?


Draw circle with the radii given below.

2 cm


Draw circle with the radii given below.

3 cm


Draw a circle with the radii given below.

4 cm


Draw a circle of any radius. Show one diameter, one radius, and one chord on that circle.


In the table below, write the names of the points in the interior and exterior of the circle and those on the circle.

Diagram Points in the interior of the circle Points in the exterior of the circle Points on the circle
     

The diameter of the circle is 52 cm and the length of one of its chord is 20 cm. Find the distance of the chord from the centre


The chord of length 30 cm is drawn at the distance of 8 cm from the centre of the circle. Find the radius of the circle


Find the length of the chord AC where AB and CD are the two diameters perpendicular to each other of a circle with radius `4sqrt(2)` cm and also find ∠OAC and ∠OCA


A chord is 12 cm away from the centre of the circle of radius 15 cm. Find the length of the chord


In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords?


Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord


A chord is at a distance of 15 cm from the centre of the circle of radius 25 cm. The length of the chord is


In the figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is


AD is a diameter of a circle and AB is a chord If AD = 30 cm and AB = 24 cm then the distance of AB from the centre of the circle is


The ratio between the circumference and diameter of any circle is _______


A line segment which joins any two points on a circle is a ___________


The longest chord of a circle is __________


The radius of a circle of diameter 24 cm is _______


A part of circumference of a circle is called as _______


Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) diameter (d) Circumference (C)
15 cm    

Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) diameter (d) Circumference (C)
    1760 cm

Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) diameter (d) Circumference (C)
  24 m  

All the radii of a circle are _______________


A line segment joining any point on the circle to its center is called the _____________ of the circle


A line segment with its end points on the circle is called a ______________


Twice the radius is ________________


Find the diameter of the circle

Radius = 10 cm


Find the diameter of the circle

Radius = 8 cm


Find the diameter of the circle

Radius = 6 cm


Find the radius of the circle

Diameter = 24 cm


Find the radius of the circle

Diameter = 30 cm


Find the radius of the circle

Diameter = 76 cm


Circles with centres A, B and C touch each other externally. If AB = 3 cm, BC = 3 cm, CA = 4 cm, then find the radii of each circle.


In the adjoining figure, seg DE is the chord of the circle with center C. seg CF⊥ seg DE and DE = 16 cm, then find the length of DF?


In figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).


Given: A circle inscribed in a right angled ΔABC. If ∠ACB = 90° and the radius of the circle is r.

To prove: 2r = a + b – c


In the figure, a circle with center P touches the semicircle at points Q and C having center O. If diameter AB = 10, AC = 6, then find the radius x of the smaller circle.


In the figure, a circle touches all the sides of quadrilateral ABCD from the inside. The center of the circle is O. If AD⊥ DC and BC = 38, QB = 27, DC = 25, then find the radius of the circle.


Circles with centres A, B and C touch each other externally. If AB = 36, BC = 32, CA = 30, then find the radii of each circle.


In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is ______ 

 


In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at point A, then ∠BAT is equal to ______.


If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.


AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = BD.


In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ______.


In figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to ______.


If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.


O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.


In figure, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.


Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.


Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how much accurate is your estimate


In the given figure, O is the centre of the circle. Name all chords of the circle.


In the given figure, O is the centre of the circle. Name a chord, which is not the diameter of the circle.


In the given figure, O is the centre of the circle. Shade the smaller segment of the circle formed by CP.


From the figure, identify the centre of the circle.

 


From the figure, identify a point in the exterior.


From the figure, identify a sector.


From the figure, identify a segment.


Is every chord of a circle also a diameter?


Draw any circle and mark

  1. it's centre
  2. a radius
  3. a diameter
  4. a sector
  5. a segment
  6. a point in its interior
  7. a point in its exterior
  8. an arc

A figure is in the form of rectangle PQRS having a semi-circle on side QR as shown in the figure. Determine the area of the plot.


A 7 m broad pathway goes around a circular park with a circumference of 352 m. Find the area of road.


If radius of a circle is 5 cm, then find the length of longest chord of a circle.


AB is a chord of a circle with centre O. AOC is diameter of circle, AT is a tangent at A.

Write answers to the following questions:

  1. Draw the figure using the given information.
  2. Find the measures of ∠CAT and ∠ABC with reasons.
  3. Whether ∠CAT and ∠ABC are congruent? Justify your answer.

Share
Notifications



      Forgot password?
Use app×