Question

Which must be true? Select two options. Point H is the center of the circle that passes through points D, E, and F.

Point H is the center of the circle that passes through points L, M, and N.
Line segment H E is-congruent-to line segment H D
Line segment L H is-congruent-to line segment N H
Line segment F L is-congruent-to line segment F N

Answer 1

A. Point H is the center of the circle that passes through points D, E, and F

C. HC≈HD

Answer 2

A. Point H is the center of the circle that passes through points D, E, and F.

C. Line segment H E is-congruent-to line segment H D

Explanation:

The center of a circle is a point within it that has the same distance to all other points on its circumference.

Constructing a circle with center H would pass through the points D, E and F at the three vertices of the given triangle. Thus producing a circumscribed circle to the triangle. A circumscribed circle is one that can is constructed outside a given figure.

It can also be observed that, DH ≅ EH ≅ FH. So that, the line segment HE is congruent to line segment HD.

The correct options in the given question are: A and C.