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Hi Phani,
This is a good problem, which will give you how to approach problems where multiple concepts have to be used.
Hint: To prove the similar triangles result, extend CD to meat AB in A'
A'D/A'P = h1/h2
====> A'D/(A'D+DP) = h1/h2
ie DP/A'D = h2/h1 - 1
and A'D/A'C = h1/h3
====> A'D/(A'D+2DP) = h1/h3
ie 2DP/A'D = h3/h1 - 1
hence 2*(h2/h1 - 1) = h3/h1 - 1
2*(h2 - h1) = h3 - h1
therefore, 2*h2 = h1 + h3.
That solves the problem.
All the Best.
Regards,
Ashwin (IIT Madras)
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