Question

In Δ ABC, BD⊥ AC and CE ⊥ AB. If BD and CE intersect at O, prove that ∠BOC = 180° − A.

Answer 1

In the given ΔABC,and .

We need prove

Here, in ΔBDC, using the exterior angle theorem, we get,

Similarly, in ΔEBC, we get,

Adding (1) and (2), we get,

Now, on using angle sum property,

In ΔABC, we get,

This can be written as,

Similarly, using angle sum property in ΔOBC, we get,

This can be written as,

Now, using the values of (4) and (5) in (3), we get,

Therefore,.

Hence proved