Question

Angle BCD is a circumscribed angle of circle A. Angle BAC measures 53°.

Circle A is shown. Line segments B A and D A are radii. Tangents B C and D C intersect at point C outside of the circle. A line is drawn to connect points A and C. Angle B A C is 53 degrees.

What is the measure of angle BCD?

37°
53°
74°
106°

Answer 1

The measurement oils be 74

Answer 2

Applying the tangent theorem, the measure of angle BCD is: 74°.

What is the Tangent Theorem?

The tangent theorem states that when a line is tangent to a circle if it forms a right angle with the radius of the circle.

Applying the tangent theorem, we would have the following:

m∠BCD = 2(180 - 90 - 53)

m∠BCD = 2(37)

m∠BCD = 74°

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