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### 1

1. 1. (1)From a point p, 10cm away from the centre of a circle, a tangent PT of length 8cm is drawn. Find the radius of the circle (CBSE 2002) (2)In the given fig,AB is a chord of length 9.6cm of a circle with centre O and radius 6cm.The tangent at A and B intersect at P.Find the length of PA (CBSE 2009C) (3) Two tangents PA and PB are drawn to a circle with centre O from an external point P.Prove that <APB=2<OAB (CBSE 2009) (4) O is the centre of two concentric circles .AB is a chord of the larger circle touching the smaller circle at C.Prove that AC=BC (CBSE 2009) (5) 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
2. 2. segments joining the points of contact to the centre. (CBSE 2008C) (6) A circle is inscribed in a triangle ABC, touching BC, CA and AB at P, Q and R respectively, as shown in the given figure. If AB=10cm, AQ=7cm and CQ=5cm, then find the length of BC (CBSE 2009C) (7) A circle is touching the side BC of triangle ABC at P and touching AB and AC produced at Q and R respectively. Prove that AQ=1/2(perimeter of triangle ABC) (CBSE 2001, 02, 06) (8)In the given fig, ABC is a right –angled triangle with AB=6cm and AC=8cm.A circle with centre O has been inscribed inside the triangle. Calculate the value of r,the radius of the inscribed circle. (CBSE 2006C)
3. 3. (9) A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB+CD=AD+BC (CBSE 2008,’08C,’09) (10) Prove that the parallelogram circumscribing a circle is a rhombus. (CBSE 2008,’09,’10) (11)In the given figure, a circle is inscribed in a quadrilateral ABCD in which <B=90 .If AD =23cm, AB=29cm and DS=5cm, find the radius of the circle (CBSE 2008) (12)In the given figure, PA is a tangent from an external point P to a circle with centre O.If<POB=115, find <APO. (CBSE 2009C)
4. 4. (13) From a point P, two tangents PA and PB are drawn to a circle C (O, r).If OP=2r, show that triangle APB is equilateral (CBSE 2008) (14) From an external point P,tangent PA and PB are drawn to a circle with centre O.If CD is the tangent to the circle at a point E and PA=14cm,find the perimeter of PCD (CBSE 2002) (15) A circle is inscribed in a triangle ABC touching AB, BC and AC are P, Q and R respectively. If AB=10cm, AR=7cm and CR=5cm, find the length of BC (CBSE 2009C)