###### Advertisements

###### Advertisements

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

###### Advertisements

#### Solution

So, the circle can have 0, 1 or 2 points in common.

The maximum number of common points is 2.

#### 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.

From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.

A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.

Fill in the blanks:

A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

Fill in the blanks:

The longest chord of a circle is a __________ of the circle.

Write True or False. Give reasons for your answers.

A chord of a circle, which is twice as long as its radius, is a diameter of the circle.

If AB, AC, PQ are tangents in Fig. and AB = 5cm find the perimeter of ΔAPQ.

From a point P, two tangents PA and PB are drawn to a circle with center O. If OP =

diameter of the circle shows that ΔAPB is equilateral.

In figure PA and PB are tangents from an external point P to the circle with centre O. LN touches the circle at M. Prove that PL + LM = PN + MN

In figure OQ : PQ = 3 : 4 and perimeter of ΔPDQ = 60cm. determine PQ, QR and OP.

Fill in the blank

Circles having the same centre and different radii are called ...........................circles.

true or false

A chord of a circle, which is twice as long is its radius is a diameter of the circle.

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

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, 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, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30° , prove that BA : AT = 2 : 1.

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.

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 60° then find the measure of ∠OAB.

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the lengths of TP and TQ.

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

In the given figure, Δ*PQR* is an isosceles triangle with *PQ* = *PR* and *m* ∠*PQR* = 35°. Find *m* ∠*QSR* and *m *∠*QTR*.

In the given figure, if *ABC* is an equilateral triangle. Find ∠*BDC* and ∠*BEC*.

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

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 13 cm and the distance from the centre is 12 cm

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

In following fig. ABC is an equilateral triangle . A circle is drawn with centre A so that ot cuts AB and AC at M and N respectively. Prove that BN = CM.

In the above figure, `square`XLMT is a rectangle. LM = 21 cm, XL = 10.5 cm. Diameter of the smaller semicircle is half the diameter of the larger semicircle. Find the area of non-shaded region.

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)

**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

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

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

Two concentric circles with center O have A, B, C, D as the points of intersection with the lines L shown in the figure. If AD = 12 cm and BC s = 8 cm, find the lengths of AB, CD, AC and BD.

In the given figure, the area enclosed between the two concentric circles is 770 cm^{2}. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

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

**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:**

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

Draw circle with diameter: 6 cm

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

Draw a circle of radius 6 cm. In the circle, draw a chord AB = 6 cm.

(i) If O is the center of the circle, join OA and OB.

(ii) Assign a special name to âˆ†AOB

(iii) Write the measure of angle AOB.

Draw a circle of radius 4.8 cm and mark its center as P.

(i) Draw radii PA and PB such that ∠APB = 45°.

(ii) Shade the major sector of the circle

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

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

Can the length of a chord of a circle be greater than its diameter ? Explain.

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 _______________

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 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.

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?

If O is the center of the circle in the figure alongside, then complete the table from the given information.

The type of arc

Type of circular arc |
Name of circular arc |
Measure of circular arc |

Minor arc | ||

Major arc |

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

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°

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 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.

A line through the point of contact and passing through centre of the circle is known as ______

If the angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre ‘O’ is 90°, then OP = ______

If d_{1}, d_{2} (d_{2} > d_{1}) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, then ______

A point P is 10 cm from the center of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal to ______

In figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the ∠RQS.

[**Hint:** Draw a line through Q and perpendicular to QP.]

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

If A, B, C and D are four points such that ∠BAC = 45° and ∠BDC = 45°, then A, B, C, D are concyclic.

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

From the figure, identify the centre of the circle.

From the figure, identify a diameter.

From the figure, identify two points in the interior.

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

- it's centre
- a radius
- a diameter
- a sector
- a segment
- a point in its interior
- a point in its exterior
- an arc

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.

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:

- 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 ______.