Question

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

EM¯¯¯¯¯¯¯¯¯≅ET¯¯¯¯¯¯¯


ED¯¯¯¯¯¯¯¯≅ER¯¯¯¯¯¯¯¯


m∠MET=90°


MD¯¯¯¯¯¯¯¯¯≅TD¯¯¯¯¯¯¯¯

Answer 1

ED ≅ ER.

Reason: If a diameter (MT) is perpendicular to a chord (DR) at E, it bisects the chord, so E is the midpoint of DR. The other statements need not hold (E is not generally the center so EM ≠ ET, ∠MET is 180° not 90°, and MD ≅ TD is not guaranteed).