The radii r1,r2,r3 of escribed circles of trisngle ABC are in HP . if area =24, perimeter =24, find a,b,c
purvi patil , 7 Years ago
Grade 11
Analytical Geometry> The radii r1,r2,r3 of escribed circles of...
1 AnswersArun
Last Activity: 7 Years ago
Area = 24
perimeter = 24, hence semi perimeter (s) = 12
r1, r2, r3 are in H.P.
hence 1/r1, 1/r2, 1/r3 will be in A.P.
1/r2 – 1/r1 = 1/r3 – 1/r2
2/r2 = 1/r1 + 1/r3
2(s – b)/ 
= (s –a)/ + (s –c)/
on solving
2s – a –c = 2(s –b)
a+b+c –a –c = 2(s –b)
b = 2(s –b)
3 b = 2s
b = 24/3
b = 8
as we know,
a+b+c = 24
a+c = 16
c= 16 – a
when applying heron’s formula,
we get,
(a –6) (a –10) = 0
a= 6 or a= 10
if a =6 , c = 10
if a =10, c= 6
hence three sides are 6,8, 10
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on analytical geometry
The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
0 Answer Available
Last Activity: 2 Years ago