In right triangle ABC with right angle at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D, such that DM = CM. Point D is joined to B. If CD = 10 cm, and BD = 6 cm, find the value of CM.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 5 cm .
A triangle ( ABC ) is a right triangle with a right angle at ( C).
( M ) is the midpoint of the hypotenuse ( AB).
( C) is joined to ( M), and line segment ( CM ) is extended to a point ( D ) such that ( DM = CM ).
( CD = 10 cm) and ( BD = 6 cm)
CD = CM + DM
CD = CM + CM = 2 × CM.
⇒ 2 × CM = 10 → CM = 5 cm.