Question

Circle C is shown. Secants A D and D J intersects at point D outside of the circle. Secant A D intersects the circle at point B and secant D J intersects the circle at point E. Angle D is 37 degrees and the measure of arc B E is 38 degrees. Secants A G and J G intersect at point G outside of the circle. Secant A G intersects the circle at point F and secant J G intersects the circle at point H. Angle G is 32 degrees.
In circle C, what is mArc F H?

31°
48°
112°
121°

Answer 1

112°

Reason: An angle formed by two secants outside a circle equals half the difference of the measures of the intercepted arcs. For ∠D,
37 = 1/2(mArc FH − mArc BE). With mArc BE = 38,
mArc FH = 2·37 + 38 = 74 + 38 = 112°.