Question

ABC is an isosceles triangle with AB = AC and ∠BAC = 40°. If a circle passing through B and C intersects sides AB and AC at D and E respectively, then ∠ADE is equal to ______.

Options

• 40°

• 50°

• 60°

• 70°

Answer 1

ABC is an isosceles triangle with AB = AC and ∠BAC = 40°. If a circle passing through B and C intersects sides AB and AC at D and E respectively, then ∠ADE is equal to 70°.

Explanation:

In isosceles triangle ABC with AB = AC and ∠BAC = 40°, each base angle is `(180° −  40°)/2 = 70°.`

Since points B and C lie on the circle, ∠BDC (an inscribed angle) intercepts arc BC, so ∠BDC = 70°.

Thus, the angle ∠ADE formed by the same arc is also 70°.