In HD

Geometry Level 3

There is a △ A B C \triangle ABC such that an altitude drawn from A A meets B C BC at D D and circumcircle at E E . If H H is the orthocentre of the triangle, then find H D HD .

R R denotes the radius of the circumcircle.

2 R cos ⁡ A cos ⁡ C 2R\cos A\cos C 2 R sin ⁡ B sin ⁡ C 2R\sin B\sin C 2 R cos ⁡ A cos ⁡ B 2R\cos A\cos B 2 R sin ⁡ B sin ⁡ A 2R\sin B\sin A 2 R cos ⁡ B cos ⁡ C 2R\cos B\cos C

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