Sadhana Bhadoriya

Ex – 10.2 Que No. 13 Q.13). Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. Solution:-

Ex – 10.2 Que No. 12 Q.12). 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 are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and

Ex – 10.2 Que No. 11 Q.11). Prove that the parallelogram circumscribing a circle is a rhombus. Solution:-

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:-