In triangle A BC with A B = A C = 5 , BC = 6 , an interior point P has distance from BC equal to the geometric mean of its distances from A B and A C . Find the minimum distance from A to the locus of

Question

In triangle A BC with A B = A C = 5 , BC = 6 , an interior point P has distance from BC equal to the geometric mean of its distances from A B and A C . Find the minimum distance from A to the locus of P .

TestHub · Accepted Answer

Set A = ( 0 , 4 ) , B = ( − 3 , 0 ) , C = ( 3 , 0 ) . The locus lies on 2 x 2 + 2 y 2 + 9 y − 18 = 0 . Its closest point to A is its upper y -axis intersection (0, 3/2), at distance 4 − 3/2 = 5/2 .

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