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)?

Answer 1

Answer:

m∠BAC = 60°

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

From the diagram, Let the midpoint of AO that lies on the circle be X

Now, XO = XB = XC (Radius of the same circle)

So, ΔXOB and ΔXOC are equilateral triangles

⇒ m∠XOC = m∠XOB = 60°

⇒ m∠BOC = 120°

Now, m∠BOC + m∠BAC = 180°

⇒ 120° + m∠BAC = 180°

⇒ m∠BAC = 60°