In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC = ?
Given: BOC is the diameter of the circle
AB = AC
Here, BAC forms a semicircle.
We know that angle in a semicircle is always 90
BAC = 90
Here ABC = ACB (since angles opposite equal sides are equal in a triangle)
We know that sum of all the angles in the triangle is 180
That is
ABC + ACB + BAC = 180
⇒ 2 × ABC + BAC = 180
⇒ 2 × ABC + 90 = 180
⇒ 2 × ABC = 180 – 90
⇒ 2 ×ABC = 90
⇒ ABC = 45