problem archive
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Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠ PTQ = 2 ∠ OPQ. -
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 length TP. -
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B... -
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to (A) 50° (B) 60° (C) ... -
Prove that the tangents drawn at the ends of a diameter of a circle are parallel. -
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. -
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. -
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. -
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC. -
In Fig. 10.13, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and... -
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joi... -
Prove that the parallelogram circumscribing a circle is a rhombus. -
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D ar... -
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. -
Let OAPB be a sector of a circle with centre O and radius r (see Fig. 11.3). Let the degree measure of ∠AOB be θ. You know that area of a circle (in f... -
Can we find the length of the arc APB corresponding to this sector? Yes. Again, by applying the Unitary Method and taking the whole length of the circ... -
Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector (Use π = 3.14). -
Find the area of the segment AYB shown in Fig. 11.6, if radius of the circle is 21 cm and \( \angle AOB = 120^\circ \). (Use \( \pi = \frac{22}{7} \)) -
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. -
Find the area of a quadrant of a circle whose circumference is 22 cm.