question_answer 100)

A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle Show that minimum length of the hypotenuse is .  

Answer:

Let in       P be a point on hypotenuse AB             PL = a, PM = b (given)       Let       L = AB = BP + AP                                      ?.. (2)                                     Now       cosec ] + a [sec3 + tan2  sec]        = b (cosec3  + cot2 cosec )             + a (sec3+ tan2 sec)              T-ratios are + ve)        is minimum when       (2)                   Hence the result.