Question

Circle D circumscribes ABC and ABE. Which statements about the triangles are true?

Answer 1

Circle D circumscribes ABC and ABE, The statements that best describe the triangles are: 
Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.
Statement II: The distance from C to D is the same as the distance from D to E. Hence, each of them (CD and DE) is a radius of the given circle.
So, the answer is the second option, I and II.

Answer 2

Answer:

I and II

Step-by-step 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.