Q4 of 53 Page 153

In ΔABC, m∠B = 90, , M. If AM — MC = 7, AB2 — BC2 = 175, find AC.


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mB = 90



AM — MC = 7


Applying Pythagoras theorem in ΔABM and ΔCBM


AB2 = BM2 + AM2 …Equation (i)


BC2 = BM2 + MC2 …Equation (ii)


Subtracting Equation (ii) from Equation (i) we get


AB2 – BC2 = AM2 – MC2


⇒ (AM – MC)(AM + MC) = AB2 – BC2


Putting the values we get :


7 × (AM + MC) = 175


⇒ AM + MC = 25


⇒ AC = 25


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