Class X : HOTS Question Answers: Math Unit - 3 (CIRCLES)

CIRCLES

A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary

In figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR

A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R respectively as shown in

Prove that the parallelogram circumscribing a circle is rhombus

Two tangents PA and PB are drawn to the circle with center O, such that ÐAPB=120o.  Prove that OP=2AP