IIT JEE , AIEEE Forum - Mathematics , Trignometry

m.viddya

Q.Let C₁ and C₂ be the inscribed and circumscribed circles of a triangle with side 3cm,4cm and 5cm.Then Area of C₁/Area of C₂=?

1.4/25

2.9/25

3.16/25

4.9/16

spideyunlimited

As it is a right angled triangle (sides 3, 4, 5)

we know that centre of circumscribed circle lies on midpoint of hypotenuse..

So it's radius is (5/2) and area is (5/2)²

Now, for inscribed circle, see attached diagram... now we can make use of the fact that two tangents drawn from a point to a circle have same length...

So

5-x + 3-x = 4

x = 2

And radius = 3 - x from figure again

so radius = 3 - 2 = 1

so area = (1)²

So area of inscribed circle / area of circumscribed circle

=

(1)² / (5/2)²

= 4 / 25

OPTION 1 IS THE ANSWER

computer001

ratio of area of circles are r^2/R^2
where r =4RsinA/2sinB/2sinC/2 where A=37,B=53 C=90
so r=4R*0.1001
r/R =0.4
(r/R)^2=0.16=4/25

eistien

ratio of the areas is given by r^2/R^2 which can be easily solved by the formulae as specified rightly by computer 001 me too getting 4/25 !!! cheers!!!

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