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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
Question

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.

A.

8 cm

B.

5 cm

C.

9.5 cm

D.

11.4 cm

Correct option is B

Given:
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.
Concept Used :
DBC is a right angled triangle Triangle ABC and DBC are congruent and and CM = 1/2 AB = CD


Solution:
∴ CM = 12×CD=12×10=5cm\frac{1}{2}× CD =\frac{1}{2}× 10 = 5 cm​​

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