Question

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

Answer 1

Answer:

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

Step-by-step 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.