Question

ABC is a triangle in which angle B=90°.M is the midpoint of AC.Prove that BM =1/2 AC.

Answer 1

Take AB = c BC = a CA = b. Now the basic thing is midpoint of hypotenuse is circumcentre i.e. M then AM = BM = CM which is b/2=√117 then b²=4(117). Here area of triangle is ac/2 and we are given a+c=30 and a²+c²=b²=4(117) then ( a+c )²=900=4(225) then a²+c²+2ac=4(225). Hence 2ac=4(108) then area ac/2=108

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