12. Prove that the parallelogram circumscribing a circle is arhombusA triangle ABC is drawn to circumscribe a circle of radius4 cm such that the segments BD and DC into which isdivided by the point of contact Dare of lengths 8 cm and6 cm respectively (see Fig. 10,19). Determine the sides ABand ACyorBВ сrm3Prove that opposite sides of a quadrilateral circumscribing º 6 cm 7D-a circle subtend supplementary angles at the centre of theFig, 10.19circle.In Fig. 10.20, BDC is a tangent to the given circle at pointDsuch that BD 3cm and CD-7cm. The other tangents 3BE and CF are drawn respectively from point B and Ctothe circle and meet when produced at A making ZBACA Eright angle triangle. Calculate (1) AF (i) radius of the circle,7A ME IFig. 10.20PR16. In Fig. 10.21 ABC is a right triangle, Aright-angled at B such that BC = 6cm and AB = 8cm find the radius ofits in circle,817. In Fig. 10.22 OQ : PQ =3:4 andimotor of APO = 60 cm. PO isPЧ y​