Question

In a right angled triangle ABC, ZACB = 90°. A circle is inscribed in the triangle with radius r. a, b, c are the lengths of sides BC,AC and AB respectively.
Prove that 2r= a +b-c

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Answer 1

Step-by-step explanation:

Answer :

since these points produce tangents at the circle, hence

AP = AQ

CP = CR

BR = BQ

Given,

AB = c

AC = b

BC = a

since CPOR is a square hence,

CP = CR = r

=> BR = BC - CR = a - r

=> BQ = BR = a - r

similarly,

AP = AC - CP = b - r

=> AQ = AP = b - r

Now,

AB = c

=> AQ + BQ = c

=> b - r + a - r = c

=> b + a - 2r = c

=> 2r = a + b - c

which is the required equation.

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Answer 2

Answer:

Answer is in pictures

Step-by-step explanation:

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