Question

A B and C are the sides of a right triangle where C is the hypotenuse a circle of radius R touches the sides of the triangle prove that R is equal to a plus b minus C the whole divided by 2 plz fast plz

Answer 1

Step-by-step explanation:

Things we need to know:

1) a² + b² = c² (Pythagoras' Theorem)

2) Δ = rs, where Δ is the area, s = (a+b+c)/2 is the semiperimeter and r is the inradius (i.e. the radius of the incircle, which is what we want to find).

3) Δ = ab/2 since it is a right angled triangle so this is just half times base times height

From (2) and (3), we have

rs = ab/2 = 2ab / 4 = ( (a+b)² - (a²+b²) ) / 4

= ( (a+b)² - c² ) / 4

= ( a+b-c ) (a+b+c) / 4    [ different of squares factorization ]

= (a+b-c) s / 2

=> r = ( a + b - c ) / 2