In Fig. 10.60, `P A` and `P B` are tangents from an external point `P` to a circle with centre `O` . `L N` touches the circle at `M` . Prove that `P L+L M=P N+M N` . (FIGURE)

In Figure, P A and P B are tangents from an external point P to a circle with centre O . L N touches the circle at M . Prove that P L+L M=P N+M N .

In Fig. 10.76, C P and C Q are tangents from an external point C to a circle with centre O . A B is another tangent which touches the circle at R . If C P=11 c m and B R=4c m , find the length of B C . (FIGURE)

In Fig. 10.96, if T P and T Q are tangents drawn from an external points T to a circle with centre O such that /_T Q P=60o , then /_O P Q= (FIGURE) 25o (b) 30o (c) 40o (d) 60o

Two tangents P Aa n dP B are drawn from an external point P to a circle with centre Odot Prove that A O B P is a cyclic quadrilateral.

Two tangents P Aa n dP B are drawn from an external point P to a circle with centre Odot Prove that A O B P is a cyclic quadrilateral.

In Fig. 10.72, P A and P B are tangents to the circle drawn from an external point P . C D is a third tangent touching the circle at Q . If P B=10 c m and C Q=2c m , what is the length P C ? (FIGURE)

PA and PB are two tangents drawn from an external point P at the points A and B on a circle with centre O.If another tangent to the circle intersects PA and PB at L and M respectively,show that LM=AL+BM.

In Fig. 10.74, C P and C Q are tangents to a circle with centre O . A R B is another tangent touching the circle at R . If C P=11 c m and B C=7c m , then find the length of B R . (FIGURE)

PA and PB are tangents from P to the circle with centre Odot At point M , a tangent is drawn cutting P A at K and P B at Ndot Prove that K N=A K+B Ndot

From a point P , two tangents P A and P B are drawn to a circle with centre O . If O P= diameter of the circle, show that /_\ A P B is equilateral.