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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

Respuesta :

Lanuel

The true statements about these triangles are: B. I and II.

How to identify the true statements?

Based on the diagram (see attachment), we can logically deduce the following points in accordance with circle theorem:

  • The tangents drawn from a point out side the circle are the same (equal).
  • The perpendicular bisectors of triangle ABC would have an intersection at the same point (center D) as those of triangle ABE.
  • The distance from point C to point D is the same as the distance from point D to point E i.e CD = DE since both are radii of the circle.

In conclusion, we can logically deduce that the true statements about these triangles are I and II only.

Read more on perpendicular bisectors here: https://brainly.com/question/16965212

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Ver imagen Lanuel

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