(see attached fig).
There is a triangle abc and an incircle to the triangle with radius 4cm.
The area of the triangle is given to be 84 cm^2
The base bc is divided by the radius into 6cm , 6cm
ab = ac
We need to find the value of these sides (ab or ac)
Methods of solving :
1)By using the pythagoras theorm, the answer comes to be appproximately 15 ( sqrrt(232) which is ~15
2)while by using area (1/2bh) the answer comes to be exactly 15..
what tis the reason for this difference?
1)Join B and C to center (say o ) of the circle..
2)Radius if perpendicular to BC ( tangent to a circle)
area of entire fig = thus area of remaining portion is 84 - 24 = 60
now join point of contact of AC and AB to O ..these will be radius and perpendicular to AB and AC respectively..
These will even be congruent ...as ab = ac & height / radius = 4cm
thus area of these =