Question

In the given diagram, O is the centre of the circle and DE is a tangent at B. If ∠ABC = 50°, then values of x, y and z respectively are:

विकल्प

• 50°, 100°, 40°

• 50°, 50°, 65°

• 40°, 80°, 50°

• 50°, 25°, 78°

Answer 1

50°, 100°, 40°

Explanation:

y = ∠AOC is the central angle subtending arc AC.

So, ∠AOC = 2 × ∠ABC   ...(Angle at centre = Twice the angle at the circumference)

= 2 × 50°

= 100°

OA = OC (radii), so triangle AOC is isosceles. 

The remaining two angles each equal `(180^circ - 100^circ)/2 = 40^circ`.

Hence, z = 40°.

By the tangent–chord theorem, the angle made by the tangent at B with a chord through B equals the angle in the opposite arc, giving x = 50°.