Sadhana Bhadoriya

Ex – 10.2 Que No. 10 Q.10). 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 joining the points of contact at the centre. Solution:-

Ex – 10.2 Que No. 9 Q.9). 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 X’Y’ at B. Prove that ∠AOB = 90°. Solution:-

Ex – 10.2 Que No. 8 Q.8). A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC Solution:-

Ex – 10.2 Que No. 7 Q.7). 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. Solution:-

Ex – 10.2 Que No. 6 Q.6). 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. Solution:-

Ex – 10.2 Que No. 5 Q.5). Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. Solution:-

Ex – 10.2 Que No. 4 Q.4). Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Solution:-

Ex – 10.2 Que No. 3 Q.3). If tangents PA and PB from a point P to a circle with center O are inclined to each other at angle of 80°, then ∠ POA is equal to Solution:-

Ex – 10.2 Que No. 2 Q.2) In Fig. 10.11, if TP and TQ are the two tangents to a circle with center O so that ∠POQ = 110°, then ∠PTQ is equal to

Ex – 10.1 Que No. 4 Q.4) Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle. Solution:-