Respuesta :

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

Answer:

The correct option is A.

Step-by-step 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,

[tex]\angle BRD=\angle BCD[/tex]

[tex]\angle BRD=57^{\circ}[/tex]                      [tex][\because C=57^{\circ}][/tex]

Therefore option A is correct.

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