Question

Given circle F with diameter GFH and LHM and JIK tangent to F at points H and I respectively. Name an angle congruent to FHM.

a. FHI
b. FIM
c. IHJ
d. LHM

Answer 1

Angle FHM is congruent to angle FHI because both are right angles formed by a tangent to the circle at the point of tangency and a radius drawn to that point.

Step-by-step explanation:

To determine an angle congruent to angle FHM, we must consider the properties of circles and tangents. Firstly, we know that a tangent at any point of the circle is perpendicular to the radius at that point. This suggests that angle FHI is a right angle (90 degrees) because HI is a tangent to circle F at point H. Since we are given that GFH is a diameter, angle FHM is also a right angle because it is an angle inscribed in a semicircle. Therefore, angle FHM is congruent to angle FHI since both are right angles.

In this context, none of the other options creates a right angle with the tangent and radius, so they cannot be congruent to angle FHM.

Thus, the correct answer is: (a) angle FHI.