Question

1. Which theorm explains why the circumcenter is equidistant from the vertices of a triangle?

a. Vertical Angles Theorem

b. Concurrency of Perpendicular Bisectors Theorem

c. Concurrency of Angle Bisector Theorem

d. Alternate Interior Angels Theorem


2. If the circumcenter of a triangle lies on the triangle, then what type of triangle is it?


a. acute

b. right

c. obtuse

d. equilateral

Answer 1

Part A:

Option B - Concurrency of Perpendicular Bisectors Theorem is the correct answer.

Concurrency of Perpendicular Bisectors Theorem states that the perpendicular bisectors of the sides of a triangle intersect in a point that is equidistant from the vertices.

Part B:

Option B- right triangle is correct.

A right-angled triangle is a triangle which have one right angle. A triangle is acute if the circumcenter lies inside the triangle and it is obtuse if the circumcenter lies outside the triangle and right if the circumcenter lies on the triangle.