In Fig., a circle touches the side DF of $\angle$EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of $\angle$EDF (in cm) is:

• 18

• 13.5

• 12

• 9

Tangents PA and PB are drawn from an external point P to two concentric circle with centre O and radii 8 cm and 5 cm respectively, as shown in Fig., If AP = 15 cm, then find the length of BP.

In fig., an isosceles triangle ABC, with AB =AB, circumscribes a circle. Prove that the point of contact P bisects the base BC.

                                            OR

In fig., the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

Prove that the parallelogram circumscribing a circle is a rhombus.

                                       OR

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

                                   OR

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.