Question

In the given figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).

Answer 1

We know that if two chords of a circle intersect each other in the interior of a circle, then the measure of the angle between them is half the sum of measures of the arcs intercepted by the angle and its opposite angle.

∴ ∠ABE = `1/2`[m(arc AE) + m(arc DC)]

∴ m(arc AE) + m(arc DC) = 2∠ABE

∴ 95º + m(arc DC) = 2 × 108°

∴ m(arc DC) = 216° − 95° = 121°

∴ The measure of arc DC is 121°.