Circle D circumscribes ABC and ABE. Which statements about the triangles are true? 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. Statement III: bisects CDE. Statement IV: The angle bisectors of ABC intersect at the same point as those of ABE. A. I only B. I and II C. II and IV D. I and III E. III and IV

The correct option is;

B. I and II

Step-by-step explanation:

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

The above statement is correct because given that ΔABC and ΔABE are inscribed in the circle with center D, their sides are equivalent or similar to tangent lines shifted closer to the circle center such that the perpendicular bisectors of the sides of ΔABC and ΔABE are on the same path as a line joining tangents to the center pf the circle

Which the indicates that the perpendicular the bisectors of the sides of ΔABC and ΔABE will pass through the same point which is the circle center D

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

The above statement is correct because, D is the center of the circumscribing circle and D and E are points on the circumference such that distance C to D and D to E are both equal to the radial length

Therefore;

The distance from C to D = The distance from D to E = The length of the radius of the circle with center D

Statement III: Bisects CDE

The above statement may be requiring more information

Statement IV The angle bisectors of ABC intersect at the same point as those of ABE

The above statement is incorrect because, the point of intersection of the angle bisectors of ΔABC and ΔABE are the respective in-centers found within the perimeter of ΔABC and ΔABE respectively and are therefore different points.

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