Secant BE and CF intersect at point A inside D. What is the measure of BF?

Question

asked Sep 28, 2019 78.4k views

1 Answer

Rebecka · Answer 1 · 2019-10-02T18:14:32+0000

Answer:

$\text{BF}=80^(\circ)$

Explanation:

We have been given a circle D. Secant BE and CF intersect at point A inside D. We are asked to find the measure of arc BF.

We know that when two secants intersect inside a circle, then the measure of angle formed is half the sum of intercepting arcs.

$m\angle EAF=\frac{\text{Measure of arc EF+Measure of arc BC}}{2}$

$70^(\circ)=\frac{\text{Measure of arc EF+Measure of arc BC}}{2}$

$2*70^(\circ)=\frac{\text{Measure of arc EF+Measure of arc BC}}{2}*2$

$140^(\circ)=\text{Measure of arc EF+Measure of arc BC}$

We know that degree measure of circumference of circle is 360 degrees, so we can set an equation as:

$\text{Arc EF+BC+EC+BF}=360^(\circ)$

$140^(\circ)+140^(\circ)+\text{BF}=360^(\circ)$

$280^(\circ)+\text{BF}=360^(\circ)$

$280^(\circ)-280^(\circ)+\text{BF}=360^(\circ)-280^(\circ)$

$\text{BF}=80^(\circ)$

Therefore, the measure of arc BF is 80 degrees.