Question

Where can the perpendicular bisectors of an acute triangle intersect?

I. Inside the triangle

II. On the triangle

III. Outside the triangle


A. I only

B. III only

C. I or III only

D. I, II, or III

Answer 1

I and II

Explanation:

Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.

Statement 1 is true because the perpendicular bisectors intersect at the center of the circumcircle.

Since the two triangles have the same circumcircle, therefore, their perpendicular bisectors intersect at the same point. So statement I is true.

Statement II: The distance from C to D is the same as the distance from D to E.

Since they both, that is distance from C to D and the distance from D to E represent the radius of the circle therefore, they both are equal in length.

Therefore, only I and II are correct.

pErIoD

Answer 2

D

Explanation: