Mathematic Worksheet - 10
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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:
3. In the given circle ABCD, O is the centre and ∠BDC = 42°. Then ∠ACB is equal to:
4.In the given figure, ∠CAB = 80°, ∠ABC = 40°. The sum of ∠DAB + ∠ABD is equal to:
5. In the given figure, if C is the centre of the circle and ∠PQC = 25° and ∠PRC = 15° , then ∠QCR is equal to:
6. In a cyclic quadrilateral if ∠B - ∠D = 60°, then the smaller of the angles B and D is:
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
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:
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
(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.
(D) None of these
11. In figure, ∠ABC = 69° , ∠ACB = 31° , ∠BDC is:
(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?
14.The value of x in the given figure is: