Question

a triangle with side lengths 26, 28, and 30 is constructed so that the longest and shortest sides are tangent to a circle. the third side passes throught the center of the circle. compute the radius of the circle

Answer 1

the area of the triangle is 336 if this helps

Answer 2

I think, since the side that is 28 passes through the center, the radius is 14.

the other two sides are tangent.

draw a pic. mine looks like an ice cream cone, and maybe you will see my thinking.

not a tutor

Answer 3

That sure helps a lot, I was working with 3 different equations, with cosine law equations and it got real messy.

Let the triangle be ABC, where AB=26, AC=30 and BC=28
The circle will have to be on the bisector of angle A, let it fall on BC at D.
Then the radius is the line from D to AB and D to AC.

Area of triangle ABC = area of ABD + area of ACD
= (1/2)(26)r + (1/2)30)r = 28r

but 28r = 336
r = 12

Answer 4

thanks reiny, not even my problem, but I couldn't stop thinking about this problem.

my pic and answer was too easy to be right!!

Answer 5

thank you so much.. this was a huge help.. and if youd like to know how i got the area of the triangle i used the formula... A=sqrt s(s-a)(s-b)(s-c) where s=a+b+c/2...a b and c are the side lengths

Answer 6

Good for you LULU, good old Heron's formula.
And good for your teacher to teach it to you!