The exradii `r_1,r_2` and `r_3` of ` /_\A B C` are in H.P. Show that its sides `a , b a n d c` are in `AdotPdot`

The ex-radii r_1,r_2,r_3 or Delta ABC are in H.P. Show that its sides a,b,c are in A.P.

The radii r_(1), r_(2), r_(3) of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24 cm^(2) and its perimeter is 24 cm, then the length of its largest side is (a) 10 (b) 9 (c) 8 (d) none of these

Lengths of the tangents from A,B and C to the incircle are in A.P., then (a) r_(1), r_(2), r_(3) are in H.P (b) r_(1), r_(2), r_(3) are in A.P (c)a, b, c are in A.P (d) cos A = (4c -3b)/(2c)

The radii r1,r2,r3 of enscribed circles of triangle ABC are in HP . If area =24, perimeter =24cm, find a,b,c.

a ,b ,c x in R^+ such that a ,b ,and c are in A.P. and b ,c and d are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

In an acute angled triangle A B C , a semicircle with radius r_a is constructed with its base on BC and tangent to the other two sides. r_b a n dr_c are defined similarly. If r is the radius of the incircle of triangle ABC then prove that 2/r=1/(r_a)+1/(r_b)+1/(r_c)dot

If in a triangle P Q R ,sinP ,sinQ ,sinR a r e i n AdotPdot , then (a)the altitudes are in A.P. (b)the altitudes are in H.P. (c)the medians are in G.P. (d)the medians are in A.P.

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a. a/c+c/a b. a/c-c/a c. b/q + q/b d. b/q - q/b

If a ,b ,c ,d in R^+ and a ,b ,c,d are in H.P., then (a) a+d > b+c (b) a+b > c+d (c) a+c > b+d (d)none of these

If vec r_1, vec r_2, vec r_3 are the position vectors of the collinear points and scalar p a n d q exist such that vec r_1=p vec r_2+q vec r_3, then show that p+q=1.