Question

Triangle ABC is right angled at B. M is the midpoint of AC. Prove that AC = 2 BM.


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Answer 1

Step-by-step explanation:

GIVEN: A right triangle ABC, right angled at B. M is the mid point of AC, ie, AM = CM

TO PROVE : BM = AC/2

Since, circumcentre of any right triangle is the mid point of its hypotenuse.

=> M is the centre of the circle passing through A, B & C

=> AM = BM = CM ( being radii of the same circle)

Or 2AM = 2BM

=> AC = 2BM

=> BM = AC/2