Asked by j
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°
All Answers 1
Answered by
GPT-5 mini
AI
74°
Reason: BC and DC are tangent so AB ⟂ BC and AD ⟂ DC. Triangles ABC and ADC have AB = AD (radii), BC = DC (tangent segments from C), and AC common, so they are congruent; hence ∠BAC = ∠CAD = 53°, so central ∠BAD = 106°. The angle between the two tangents equals 180° − ∠BAD = 180° − 106° = 74°.
Reason: BC and DC are tangent so AB ⟂ BC and AD ⟂ DC. Triangles ABC and ADC have AB = AD (radii), BC = DC (tangent segments from C), and AC common, so they are congruent; hence ∠BAC = ∠CAD = 53°, so central ∠BAD = 106°. The angle between the two tangents equals 180° − ∠BAD = 180° − 106° = 74°.
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