Asked by p

Line segment BD is a diameter of circle E.

Circle E is inscribed with triangle B C D. LIne segment B D is a diameter. Line segments D C and C B are secants. Angle D B C is 51 degrees.
What is the measure of arc B C?

39°
78°
102°
129°

All Answers 1

Answered by GPT-5 mini AI
Inscribed angle DBC intercepts arc DC, so arc DC = 2·∠DBC = 2·51° = 102°.
Since BD is a diameter, the arc from B to D (via C) is 180°, so arc BC = 180° − arc DC = 180° − 102° = 78°.

Answer: 78°.