Question

In a triangle ABC, let angle C be 90 degrees. a,b and c are sides of triangle opposite to angles A,B and C respectively. If r is in-radius and R is the circumradius of the triangle ABC, the 2(R + r) equals​

Answer 1

Answer:

Tangents drawn from external points are of equal length.

Tangents drawn from external points are of equal length.⇒BD=BE=a−r [∵CD=r]

Tangents drawn from external points are of equal length.⇒BD=BE=a−r [∵CD=r]and AF=AE=b−r [∵CF=r]

Tangents drawn from external points are of equal length.⇒BD=BE=a−r [∵CD=r]and AF=AE=b−r [∵CF=r]∵AE+BE=AB

Tangents drawn from external points are of equal length.⇒BD=BE=a−r [∵CD=r]and AF=AE=b−r [∵CF=r]∵AE+BE=AB⇒b−r+a−r=2R [∵ AB is a diameter of circumcircle]

Tangents drawn from external points are of equal length.⇒BD=BE=a−r [∵CD=r]and AF=AE=b−r [∵CF=r]∵AE+BE=AB⇒b−r+a−r=2R [∵ AB is a diameter of circumcircle]⇒b+a=2R+2r2(r+R)=a+b