Let triangle ABC have altitude `h_a, h_b, h_c` from points `A, B, C` respectively. If `h_a = 8, h_b = 8, h_c= 10`, then the length of side AB can be expressed as `p/sqrtq`(where p, q are natural numbers). Find the minimumvalue of `(p+q)`.

In the adjacent figure 'P' is any arbitrary interior point of the triangle ABC. H_a,H_b and H_c are the length of altitudes draw from vertices A,B and C respectively. If x_a,x_b and x_c represent the distance of 'P' from sides BC, CA and AB respectively, then the minimum value of (H_a/x_a+H_b/x_b+H_c/x_c) must be

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

If a , b , c are in H.P. , then

If in a triangle ABC, the altitudes from the A,B,C on opposite sides are in H.P. then sinA, sin B, sin C are in

If in a !ABC , the altitudes from the vertices A , B , C on the opposite sides are in H.P., then sin A, sin B , sin C are in

If in a DeltaABC , the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in

If in a DeltaABC , the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in

If a ,b ,c are the p t h ,q t h ,r t h terms, respectively, of an H P , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.

If a ,b ,c are the p t h ,q t h ,r t h terms, respectively, of an H P , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.