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What is the radius of the inscribed circle to a triangle [#permalink]

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27 Jan 2004, 13:19

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What is the radius of the inscribed circle to a triangle whose sides measure
21cm, 72cm and 75cm respectively?
(1) 9 cm
(2) 37.5 cm
(3) 28.5 cm
(4) 14.5 cm _________________

There is a formula for this but I dont remember. as we know the area of the triangle is 1/2 base * height and so the area is 1/2*21*76 = 756 and the area of the circle is phi r^2 which should be less than 756. So of the choices 37.5 and 28.5 is ruled out. Now left with 9 and 14. These can be the answers, in exam I would opt for 9 as the area is less and also is a multiple of 3 like the sides 21,72 and 75.

Since this is a right triangle the area is 21x72/2=756. The area of a triangle that has a circle inscribed is S=pr ( p-half the perimeter of triangle, r-radius of inscribed circle).P=168,(21+75+72) ,p=P/2=84 Then 756/84= r =9

Guys,
there is quick way to approximate right choice in this particular case.

You see, the diameter of incribed circle CANNOT be more than the least of the sides of a triangle. So the most value of the radius might be is 21/2=10.5 sm. Therefore, I pick (1) w/o any calculations.

General advice. See choices before rush into calculus.

Thank you. I agree with you on this given the choices. I was looking for radius < 21 and that was my error. But, what if both 9 and 10 were given in the choices?

I'd rather know of a property that helps me in the long run.