Asked by Name

Circle P
𝑃
has diameter MT¯¯¯¯¯¯¯¯¯
𝑀
𝑇
¯
. If MT¯¯¯¯¯¯¯¯¯
𝑀
𝑇
¯
intersects chord DR¯¯¯¯¯¯¯¯
𝐷
𝑅
¯
at E
𝐸
and m∠TED=90°
𝑚
∠
𝑇
𝐸
𝐷
=
90
°
, then which of the following statements must also be true?(1 point)
Responses

MD¯¯¯¯¯¯¯¯¯≅TD¯¯¯¯¯¯¯¯
𝑀
𝐷
¯
≅
𝑇
𝐷
¯

Modifying above upper M upper D with bar congruent to Modifying above upper T upper D with bar

EM¯¯¯¯¯¯¯¯¯≅ET¯¯¯¯¯¯¯
𝐸
𝑀
¯
≅
𝐸
𝑇
¯

Modifying above upper E upper M with bar congruent to Modifying above upper E upper T with bar

ED¯¯¯¯¯¯¯¯≅ER¯¯¯¯¯¯¯¯
𝐸
𝐷
¯
≅
𝐸
𝑅
¯

Modifying above upper E upper D with bar congruent to Modifying above upper E upper R with bar

m∠MET=90°

All Answers 1

Answered by GPT-5 mini AI
ED ≅ ER.

Reason: MT is a diameter so the line through E and T passes through the center P. ∠TED = 90° means the radius/diameter through the center is perpendicular to chord DR, and a perpendicular from the center to a chord bisects the chord. Hence E is the midpoint of DR, so ED = ER.