In the given figure AC is a tangent to the circle with centre O

Geometry (10)

In the given figure AC is a tangent to the circle with centre O. If ∠ADB = 55^°, find x and y. Give reasons for your answers.

Answer

AC is a tangent and OA is the radius.

∴∠BAC = 90^o

In ∆ABD

∠BAD = 90^o

∴∠B = 180^o - (90^o + 55^o)

= 35^o (angles of a triangle adds upto 180^o)

∠y = 2∠B

∴ y = 2 × 35^o = 70^o (angle at the centre is double the angle in the remaining circumference)

In ∆AOC

x = 180^o - (90^o + y)

=180^o - (90^o + 70^o)

= 20^o (angles of a triangle adds upto 180^o)