Practice Questions for Geometry - Circles

1. PE 2 - Circles | Geometry - Circles

A is a point outside a circle of radius 5 cm and two tangents AP and AQ are drawn. Line joining point A with center of the circle O cuts the circle at D and is 13 cm long. The tangent drawn from D intersects the AP and AQ at points B and C respectively. Find the length of BC.

(a)
10/3
(b)
20/3
(c)
3
(d)
None of these

2. PE 2 - Circles | Geometry - Circles

In the figure below, AB = 32 cm and is tangent to the two smaller circles. Find the area of the shaded part (in cm²). All three circles touch each other.

(a)
128
(b)
32π
(c)
64π
(d)
128π
(e)
Cannot be determined

3. PE 2 - Circles | Geometry - Circles

In the figure given below, radius of the circle is √3 cm. What is the length of CE given that CE || OA, DE || BO and ∠AOB = 60°.

(a)
1.5 cm
(b)
3√3/2 cm
(c)
√3 cm
(d)
2 cm

4. PE 2 - Circles | Geometry - Circles

In the given figure (not drawn to scale), a semicircle with its diameter on the hypotenuse of a right-angled triangle is drawn touching the remaining sides of the triangle. The two parts of the hypotenuse made by the centre of the semicircle have lengths 24 cm and 32 cm respectively. Find the radius of the semicircle (in cm).

[Type your answer as the neared possible integer]

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7 8 9 4 5 6 1 2 3 0 . -

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5. PE 2 - Circles | Geometry - Circles

In the figure below, AB is a diameter of the circle and C and D are such points that CD = BD. AB and CD intersect at O. If angle AOD = 35°, find angle ADC (in degrees).

(a)
30
(b)
40
(c)
50
(d)
60

6. PE 2 - Circles | Geometry - Circles

In the figure given below, PR and ST are perpendicular to tangent QR. PQ passes through center O of the circle whose diameter is 10 cm. If PR = 9 cm, then what is the length (in cm) of ST?

(a)
1
(b)
1.25
(c)
1.2
(d)
2

7. PE 2 - Circles | Geometry - Circles

In the figure given below, a smaller circle touches a larger circle at P and passes through its center O. PR is a chord of length 34 cm, then what is the legth (in cm) of PS?

(a)
9
(b)
17
(c)
21
(d)
25

8. PE 2 - Circles | Geometry - Circles

In the figure given below, ABC is a triangle in which AB = 10 cm, AC = 6 cm and altitude AE = 4 cm. If AD is the diameter of the circum-circle, then what is the legth (in cm) of circum-radius of triangle ABC?

(a)
3
(b)
7.5
(c)
12
(d)
15

9. PE 2 - Circles | Geometry - Circles

In the figure, ACB is a right triangle. CD is the altitude. The circles are inscribed within the triangles ACD and BCD. P and Q are the centres of the circles. Find the distance PQ.

(a)
5
(b)
6
(c)
5√2
(d)
8

10. PE 2 - Circles | Geometry - Circles

In the figure given below, smaller circle touches bigger circle at point C. A is the center of bigger circle while B is the center of smaller circle. ∠ABE = 45°. If BC = 3 cm, find DE

(a) $\frac{3 \sqrt{7} - 3}{2}$
(b)
$\frac{3 \sqrt{7} + - 3 \sqrt{2} + 3}{\sqrt{2}}$
(c)
$\frac{3 \sqrt{7} + 3}{\sqrt{2}}$
(d)
None of these

PE 2 - Circles | Geometry - Circles

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