CLASS-10

BOARD: CBSE

Mathematic Worksheet - 10

TOPIC: Circle

For other **CBSE Worksheet for class 10 Mathematic** check out main page of Entrancei.

**SUMMARY**

Theorem 1: The perpendicular from the centre of a circle to a chord bisects the chord.

Theorem 2: There is one and only one circle passing through three given non-collinear points.

Theorem 3: the angle subtended by an arc at the centre is double the angle subtended by it at any

point on the remaining part of the circle.

Theorem 4: Angles in same segment of a circle are equal.

Theorem 5: angle in the semicircle is a right angle.

Theorem 6: the sum of either pair of opposite angles of a cyclic quadrilateral is 180°.

Theorem 7: Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centers).

Theorem 8: A tangent to a circle is perpendicular to the radius through the point of contact.

Theorem 9: Lengths of two tangents drawn from an external point to a circle are equal.

**1. In a circle of radius 10 cm, the length of chord whose distance is 6 cm from the centre is:**

(A) 4 cm

(B) 5 cm

(C) 8 cm

(D) 16 cm

**2. If a chord of length 8 cm is situated at a distance of 3 cm from centre, then the diameter of circle is:**

(A) 11cm

(B)10cm

(C) 12cm

(D) 15cm

**3. In the given circle ABCD, O is the centre and ∠BDC = 42°. Then ∠ACB is equal to:**

A. 48°

(B) 45°

(C) 42°

(D) 60°

**4.In the given figure, ∠CAB = 80°, ∠ABC = 40°. The sum of ∠DAB + ∠ABD is equal to:**

(A) 80°

(B) 100°

(C) 120°

(D) 140°

**5. In the given figure, if C is the centre of the circle and ∠PQC = 25° and ∠PRC = 15° , then ∠QCR is equal to:**

A. 40°

(B) 60°

(C) 80°

(D) 120°

**6. In a cyclic quadrilateral if ∠B - ∠D = 60°, then the smaller of the angles B and D is:**

A. 30°

(B) 45°

(C) 60°

(D) 75°

**7. In the diagram two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. Find the length of the common chord.**

(A) 2 √3 cm

(B) 4 √3 cm

(C) 4√3 cm

(D) 8cm

**8. The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to:**

A.30°

(B) 45°

(C) 60°

(D) 90°

**9. The length of the tangent drawn from a point 8 cm away from the centre of a circle of radius 6 cm is:**

(A) √7 cm

(B)2√7 cm

(C) 10 cm

(D) 5 cm

**10. In a circle radius of 5 cm, AB and AC are two chords such that AB = AC = 6 cm. find the length of the chord BC.**

A.9.6

(B) 4.8

(C) 10

(D) None of these

**11. In figure, ∠ABC = 69° , ∠ACB = 31° , ∠BDC is:**

(A) 80°

(B) 75°

(C) 90°

(D) None of these

**12.Two parallel chords AB and CD, of lengths 6 cm and 8 cm respectively, are 1 cm apart. The radius of the circle is :**

(A) 2.5 cm

(B) 4 cm

(C) 5 cm

(D) 5.5 cm

**13.In the adjoining figure, x : y is equal to, where O is centre of circle?**

(A)1:1

(B) 2:1

(C) 3:2

(D) 1:4

**14.The value of x in the given figure is:**

(A) 30°

(B) 20°

(C) 10°

(D) 40°