Question

AB and AC are tangent segments of circle k(O). What is the measure of the angle ∠BAC, if midpoint of AO lies on the circle k(O)?

m∠BAC=

Answer 1

60°

Explanation:

B and C are the points of intersection of the circle with diameter AO with circle O. If the midpoint of AO is X on circle O, then XO = XB = XC and ΔXOB and ΔXOC are equilateral triangles. That makes ∠BOC = 120° and its supplement, ∠BAC, equal to 60°.