IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

rahulraj1

Let ABCD be a quadilateral with area 18, with side AB parallel to the side CD and AB=2CD.Let AD be perpendicular to AB and CD.If a circle is drawn inside the quadilateral ABCD touching all the sides ,Then what is its radius.

pink_ele

AB PARALLEL TO CD
n circle touches all 4 side
so ab n cd r two parralel tangents
that is distance between dem is daimeter
so r=da/2
now its a trapzoid so area=18=1/2x da x(ab +cd)
also when it touches all 4 sides ab+cd=bc+da (10th ki property hai)
3cd=da+bc
further
bc=rt ad^2+cd^2
solving all dis u get
8 cd^2=6(ad x cd )
ad=4/3
r=2/3

rahulraj1

You are wrong and ans. is 2

RyuAmakusa

yes ans.is 2 area of quad is 18 let AB =x so we get rx = 6 where r is the radius.

now this part is diff. to exp. without diag. any way i'll try my best.

drop a perp. from B to CD let it meet at E now CE = ED = x now you apply the

prop. that tangents from ext pt are =. you get BD 3x - 2r in tri. BED apply phy.

theorm (3x-2r)²= x² + 4r² => 2x= 3r now sub x=6/r. =>r=2.

if it is not clear i will post the diag.

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