Question

In a triangle ABC, ∠ACB = 36°, H is the orthocentre. Altitude drawn from A meets the circumcircle of ΔABC in D. Let ∠HBD = θ. Find the sum of digits of θ.

Answer 1

Answer:

Consider, △BHN and △BDN

∠C=∠C

BN=BN

∠BNH=∠BND [Right-angled angle]

△BHN and △BDN are congurent

hence , HN=ND=2RcosBcosC

HD=2HN

HD=4RcosBcosC

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