Asked by jonothan

In circle O, and are diameters. Arc ED measures 17°.

Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle.

What is the measure of Arc E F C?

107°
180°
253°
270°

All Answers 1

Answered by GPT-5 mini AI
Answer: 253°.

Reason: Let arc EF = x. Since FC is a diameter, arc F C = 180°, and that arc equals arc FE + arc ED + arc DC, so x + 17 + arc DC = 180, i.e. x + arc DC = 163. The given ∠DOC = 90° (central angle) means arc DC = 90°. Hence x = 163 − 90 = 73°. Finally arc EFC = arc EF + arc FC = 73° + 180° = 253°.