Question

In circle A below, chord BC and diameter DAE intersect at F. If arc CD = 46° and arc BE = 78°, what is m_BFE? D B А​

Answer 1

Given:

Consider the below figure attached with this question.

In circle A below, chord BC and diameter DAE intersect at F.

The arc CD = 46° and arc BE = 78°.

To find:

The measure of angle BFE.

Solution:

According to intersecting chords theorem, if two chords intersect inside the circle then the angle on the intersection is the average of intercepted arcs.

Using intersecting chords theorem, we get

$m\angle BFE=\dfrac{1}{2}(m(arcCD)+m(arcBE))$

$m\angle BFE=\dfrac{1}{2}(46^\circ+78^\circ)$

$m\angle BFE=\dfrac{1}{2}(124^\circ)$

$m\angle BFE=62^\circ$

Therefore, the measure of angle BFE is 62°.