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
6 answers
the area of the triangle is 336 if this helps
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
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
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
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
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!!
my pic and answer was too easy to be right!!
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
Good for you LULU, good old Heron's formula.
And good for your teacher to teach it to you!
And good for your teacher to teach it to you!