Circles ncert solutions Chapter 10 Exercise 10.2 Question 9
9. XY and X’Y’ are two parallel tangents to a circle with center O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that
.
Solution:
and
AO=AO {Common}
AC = AP {Tangents drawn from an external point to a circle are equal}
OC=OP {Radii of same circle are equal}
Therefore,
{Corresponding angles of congruent triangles are equal} (1)
Similarly, in
and
, we can prove that
(2)
Also,
{Linear pair}
Putting (1) and (2) in the above equation, we get
Hence Proved
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