Radius

Q.

In a right triangle $ABC$, right-angled at $B,BC=12$ cm and $AB=5$ cm. The radius of the circle inscribed in the triangle is

(a) $1$ cm (b) $2$ cm (c) $3$ cm (d) $4$ cm

Q. If the perimeter of a semi-circular protractor is 36 cm, then its diameter is

(a) 10 cm

(b) 12 cm

(c) 14 cm

(d) 16 cm

Q.

P & Q are centres of circles of radius 9cm and 2cm respectively. PQ = 17cm. R is the centre of a circle of radius x cm, which touches the above circles externally. Given angle PRQ = 90⁰, write an equation in x and solve it.

1. 3cm

2. 6cm

3. 12cm

4. 18cm

5. 4.5cm

Q.

Three circles with centres A, B and C touch each other externally. If, AB = 5cm, BC = 7 cm and CA = 6 cm. Find the radii of the circles.

Q.

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.

Q.

In fig., two circles with centres A and B touch each other externally at k. The length of PQ (in cm) is

1. 27 cm

2. 24 c

3. 20 cm

4. 18 cm

Q. Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.

Q.

Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centres if :

(i) they touch each other externally,

(ii) they touch each other internally.

Q. Question 1 (vi)
Fill in the blanks:

(vi) A circle divides the plane, on which it lies, in to __________ parts.

Q. A chord of a circle which is twice the radius of the circle is the diameter of the circle.

1. True
2. False

Q.

State whether the following statements are true or false.

a) There is an infinite number of radii in a circle.

1. True
2. False

Q. A diameter subtends an angle of ${90}^{\circ }$ at the circumference of the circle.

1. False
2. True

Q.

The given figure shows two circles with centres A and B; and radii 5 cm and 3 cm respectively, touching each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.

Q.

In the given figure, three circles with centres A, B, C respectively touch each other externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm then the radius of the circle with centre A is

(a) 1.5 cm (b) 2 cm

(c) 2.5 cm (d) 3 cm

Q.

In the given figure, two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that

(i) ΔPAC ∼ ΔPDB

(ii) PA.PB = PC.PD

Q.

A circle of radius 3 cm, with centre O is drawn circumscribing a $\Delta$ABC. What is the sum of OA + OB + OC?

1. 6 cm

2. 3 cm

3. 12 cm

4. 9 cm

Q.

Three circles touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides fo the triangle formed are 6 cm, 8 cm and 9 cm.

Q. In a right triangle ABC, right angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle is [CBSE 2014]
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

Q.

In ∆ PQR, PQ = 24 cm, QR = 7cm & /PQR = 90^o. Find the radius of the inscribed circle.

1. 4 cm

2. 2.5 cm

3. 1 cm

4. 2 cm

5. 3 cm

Q.

In the figure given below AB = 7 cm BC = 8 cm CA = 5 cm. What are the radii of the circles A, B and C?

1. 2 cm, 4 cm and 5 cm

2. 1 cm, 3 cm and 7 cm

3. 2 cm, 5 cm and 3 cm

4. 1 cm, 3 cm and 4 cm

Q. If two circles with radius a cm and b cm meet externally., then the distance between their centres is equal to ______ cm.

1. $a+b$
2. $a-b$
3. $a\times b$
4. $\frac{a}{b}$

Q. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.

Q. If a rope of length 15π m is bent to form a circle, then what is the radius of the circle formed?

1. 7.5 m
2. 15 m
3. 15$\pi$ m
4. 30 m

Q.

What is the circumference of a circle of radius 7 cm?

1. 198 cm

2. 19.8 cm

3. 22 cm

4. 66 cm

Q. In the given figure ∆ABC is right-angled at A, with AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Find the value of r, the radius of the inscribed circle.

Q. If the circumference and the area of a circle are numerically equal, then diameter of the circle is

(a) $\frac{\mathrm{\pi }}{2}$

(b) 2$\mathrm{\pi }$

(c) 2

(d) 4

Q. Find the radius of the circle passing through the vertices of a right angled triangle when length of perpendicular sides are 6 and 8.

Q.

The radius of the circle is 6cm. The circle touches another circle externally and the distance between their centres is 10cm. What is the radius of the second circle?

Q. In the given circle with centre O, if the radius of the circle is 13 cm, OQ⊥PR and OQ = 5 cm. Find PR.

1. 5 cm
2. 24 cm
3. 13 cm
4. 12 cm

Q. Suppose P, Q are two points on the same side of the line AB, R is a point on the segment PQ such that PR = (lambda) * PQ. Prove that Area of ABR = Area of ABP * (1-lambda) + (lambda) * Area of ABQ.