Question

Point D is the incenter of triangle BCA. If m∠FDG = 128°, what is the measure of ∠FHG? Triangle BCA with inscribed circle D. Segments BF and BH, CF and CG, and AG and GH are tangent to circle D; segments FD, GD, FH, and GH are created from points F, G, D, and H.

a. 32°
b. 52°
c. 64°
d. 128°

Answer 1

In triangle BCA, point D is the incenter. The measure of angle FHG is c) 64°.

Step-by-step explanation:

Incenter is the point of concurrency of the angle bisectors of a triangle. In triangle BCA, point D is the incenter, which means that the angle bisectors BF, CF, and AG intersect at point D.

Since FD and GD are tangent to circle D, m∠FDG = 128°. By the tangent-chord theorem, ∠FHG is half of ∠FDG, so m∠FHG = m∠FDG/2 = 128°/2 = 64°.

Therefore, the measure of ∠FHG is 64°, so the correct answer is c. 64°.