Question

If ABC is an acute-angled triangle with circumcenter O and Orthocenter H. If AO = AH, then angle A = .

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{8}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C $\frac{\pi }{3}$

OA = HA
$⟹$ R = 2R cos A
$⟹$cos A = $\frac{1}{2}$
$⟹$ A = $\frac{\pi }{3}$