###### Advertisements

###### Advertisements

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

###### Advertisements

#### Solution

Length of the chord = 20 cm

AC = `20/2`

= 10 cm

In ΔOAC, OC^{2} = OA^{2} – AC^{2}

= 26^{2} – 10^{2}

= (26 + 10)(26 – 10)

= 36 × 16

OC = `sqrt(30 xx 16)`

= 6 × 4 cm

= 24 cm

Distance of the chord from the centre = 24 cm.

#### APPEARS IN

#### RELATED QUESTIONS

Points A(–1, *y*) and B(5, 7) lie on a circle with centre O(2, –3*y*). Find the values of* y*. Hence find the radius of the circle.

ABC is a right triangle, right angled at B. A circle is inscribed in it. The lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the incircle.

Fill in the blanks:

The centre of a circle lies in ____________ of the circle.

O is the center of a circle of radius 8cm. The tangent at a point A on the circle cuts a line through O at B such that AB = 15 cm. Find OB

If from any point on the common chord of two intersecting circles, tangents be drawn to circles, prove that they are equal.

If PA and PB are tangents from an outside point P. such that PA = 10 cm and ∠APB = 60°. Find the length of chord AB.

In fig.. O is the center of the circle and BCD is tangent to it at C. Prove that ∠BAC +

∠ACD = 90°

In fig. there are two concentric circles with Centre O of radii 5cm and 3cm. From an

external point P, tangents PA and PB are drawn to these circles if AP = 12cm, find the

tangent length of BP.

In the given figure, *AB* is a chord of length 16 cm of a circle of radius 10 cm. The tangents at *A* and* B* intersect at a point *P*. Find the length of *PA*.

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, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; Find:

(i) ∠ACB, (ii) ∠OBC, (iii) ∠OAB, (iv) ∠CBA.

In the following figure, AB is the diameter of a circle with centre O and CD is the chord with length equal to radius OA.

Is AC produced and BD produced meet at point P; show that ∠APB = 60°

If PT is a tangent to a circle with center O and PQ is a chord of the circle such that ∠QPT = 70°, then find the measure of ∠POQ.

The circumference of a circle is 22 cm. The area of its quadrant (in cm^{2}) is

In figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P.

If ∠POQ = 70°, then ∠TPQ is equal to

A chord of a circle of radius 14 cm subtends an angle of 120° at the centre. Find the area of the corresponding minor segment of the circle. `[User pi22/7 and sqrt3=1.73]`

In a cyclic quadrilateral *ABCD* if *AB* || *CD* and ∠*B** *= 70°, find the remaining angles.

In the given figure, if ∠*BAC** *= 60° and ∠*BCA* = 20°, find ∠*ADC*.

In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

In the given figure, common tangents *PQ* and *RS* to two circles intersect at *A*. Prove that *PQ* = *RS.*

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 1. 7cm and the distance from the centre is 1.5 cm

If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

Find the area of a circle of radius 7 cm.

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

**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.**

Find the area of the shaded region in the figure If ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. (Take π= 3.14)

ABC is a right triangle in which ∠B = 90°. If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.

In an equilateral triangle, prove that the centroid and center of the circum-circle (circumcentre) coincide.

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

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:**

Tangent to a circle is _______.

**Use the figure given below to fill in the blank:**

EF is a ______ of the circle.

**Use the figure given below to fill in the blank:**

________ is a radius of the circle.

**Use the figure given below to fill in the blank:**

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

**Use the figure given below to fill in the blank:**

AB is a ______ of the circle.

Draw circle with diameter: 6 cm

In above case, measure the length of the radius of the circle drawn.

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 ABC with AB = 5 cm, ∠B = 60° and BC = 6. 4 cm. Draw the incircle of the triangle ABC.

**State, if the following statement is true or false:**

The longest chord of a circle is its 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 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 _______________

The ______________ is the longest chord of a circle

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 = 30 cm

Find the radius of the circle

Diameter = 76 cm

A, B, C are any points on the circle with centre O. If m(arc BC) = 110° and m(arc AB) = 125°, find measure arc AC.

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).

In figure, O is the centre of a circle, chord PQ ≅ chord RS. If ∠POR = 70° and (arc RS) = 80°, find

(i) m(arc PR)

(ii) m(arc QS)

(iii) m(arc QSR)

In the figure, segment PQ is the diameter of the circle with center O. The tangent to the tangent circle drawn from point C on it, intersects the tangents drawn from points P and Q at points A and B respectively, prove that ∠AOB = 90°

**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 a circle with centre P, chord AB is parallel to a tangent and intersects the radius drawn from the point of contact to its midpoint. If AB = `16sqrt(3)`, then find the radius of the circle

In the figure, O is the center of the circle. Line AQ is a tangent. If OP = 3, m(arc PM) = 120°, then find the length of AP.

In the figure, O is the centre of the circle, and ∠AOB = 90°, ∠ABC = 30°. Then find ∠CAB.

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.

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 ______

If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF = BC + DE + FA.

AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is ______.

In figure, if ∠OAB = 40º, then ∠ACB is equal to ______.

In figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to ______.

A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.

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.

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

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 all radii 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.

From the figure, identify the centre of the circle.

From the figure, identify three radii.

From the figure, identify a diameter.

From the figure, identify a sector.

From the figure, identify a segment.

Is every diameter of a circle also a chord?

Say true or false:

Two diameters of a circle will necessarily intersect.

Say true or false:

The centre of a circle is always in its interior.

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 an are subtends an angle of 90° at the centre of a circle, then the ratio of its length to the circumference of the circle is ______.

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:

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

The circumcentre of a triangle is the point which is ______.