# Thread: Area of a triangle

1. ## Area of a triangle

This question regards a circle inside a triangle, there are 3 parts to the question and i cannot do any of them but i think if i could do part a) then maybe i could do the rest, if somebody could please help me.

Q: A right angled triangle with sides a, b and c where a<b<c contains a circle such that the circle just touches all sides of the triangle. The circle has radius of 1cm.

a) show that ab=a+b+c

b) show that a+b=c+2

c)deduce that the area of the triangle is (a+b-1)

any help would be great, thanks.

2. Originally Posted by wahhdoe
This question regards a circle inside a triangle, there are 3 parts to the question and i cannot do any of them but i think if i could do part a) then maybe i could do the rest, if somebody could please help me.

Q: A right angled triangle with sides a, b and c where a<b<c contains a circle such that the circle just touches all sides of the triangle. The circle has radius of 1cm.

a) show that ab=a+b+c
Hi

The area of the triangle is ab/2
It is also the sum of the 3 triangles : aR/2 + bR/2 + cR/2 where R is the radius of the circle
Therefore ab = R(a+b+c)
And since R=1
ab = a+b+c

3. ok thanks, the diagram was very useful, it helped me visualize the question which helped alot.

but even after knowing part a) i am still unable to solve b) and c) would you also be able to help with these parts of the question?

4. ## area of a triangle

Originally Posted by wahhdoe
This question regards a circle inside a triangle, there are 3 parts to the question and i cannot do any of them but i think if i could do part a) then maybe i could do the rest, if somebody could please help me.

Q: A right angled triangle with sides a, b and c where a<b<c contains a circle such that the circle just touches all sides of the triangle. The circle has radius of 1cm.

a) show that ab=a+b+c

b) show that a+b=c+2

c)deduce that the area of the triangle is (a+b-1)

any help would be great, thanks.
Hi wahhdoe,
You have part a. I deduce that a,b,c is 3,4,5 and calculate the angle opposite a is 36.8 and its tangent is 3/4. Makes question b and c correct.
In center radius is 1 and the tangent of 36.8/2 = 1/3

bjh

5. ab = a+b+c
a+b = ab-c
Square both sides
a²+2ab+b² = a²b²-2abc+c²
And since a²+b²=c²
2ab = a²b²-2abc
a and b being not equal to 0 we can divide by ab
2 = ab - 2c
But ab = a+b+c
a+b-c = 2
a+b = c+2