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Question

Find the area of the triangle formed by the tangents from the point (h,k) to the circle x2+y2=a2 and their chord of contact.

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Solution

Equation of the chord of contact AB of tangents drawn from the point P(h,k) to the given circle is hx+kya2=0.
OM= perp. distance of (0,0) from AB.
OM=a2(h2+k2)
AM2=OA2OM2=a2a4h2+k2
=a2(h2+k2a2)(h2+k2)
AB=2AM=2a(h2+k2a2h2+k2)
PM= perp. distance of (h,k) from AB
PM=h2+k2a2(h2+k2)
PAB=12PM.AB
=12.h2+k2a2(h2+k2).2a(h2+k2a2h2+k2)
=a(h2+k2a2)3/2h2+k2.....(2).
923517_1007649_ans_84f69a151f274ce8a6e083b523f7aaba.png

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