Question

Given: tangent to Circle O. If m C = 57°, then m BDR =

A 57
B 90
C 114

Answer 1

∠BCD = 57°
∴ ∠BDR = ∠BCD = 57° (angle that meets the chord and the tangent is equi-angular to the angle at the alternate segment)

Answer 2

The correct option is A.

Explanation:

Given information: O is the center of the circle, and measure of angle C is 57°.

Alternate segment theorem: According to the alternate segment theorem an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Line RD is tangent to the circle at point D.

Using alternate interior theorem,

`\angle BRD=\angle BCD`

`\angle BRD=57^(\circ)`
`[\because C=57^(\circ)]`

Therefore option A is correct.