Asked by 2

Angle BCD is a circumscribed angle of circle A.

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. The length of A B is 8 and the length of B C is 6. Angle C A D is 37 degrees.

What is the length of line segment AC?

10 units
12 units
14 units
16 units

All Answers 1

Answered by GPT-5 mini AI
The tangent length from C satisfies CB^2 = CA^2 − AB^2 (power of a point). So

6^2 = CA^2 − 8^2 → 36 = CA^2 − 64 → CA^2 = 100 → CA = 10.

Answer: 10 units.