Q8 of 53 Page 158

In ΔABC, , D and ∠B is right angle. If AC = 5CD, prove that BD = 2CD.


ΔABC is a right triangle, right angle at B and BD is perpendicular from B vertex to hypotenuse AC.


So, as we know that,


If an altitude is drawn to hypotenuse of a right angled triangle, then the length of altitude is the geometric mean of lengths of segments of hypotenuse formed by the altitude.


⇒ BD2 = AD.CD


⇒ BD2 = (AC – CD).CD


As, AC = 5CD,


⇒ BD2 = (5CD – CD).CD


⇒ BD2 = 4CD2


⇒ BD2 = (2CD)2


⇒ BD = 2CD


Hence, proved.


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