Question

In △ABC, B = 90. Prove that a + c = 2r + 2R where lengths

of side BC, CA, AB are a, b, c respectively and r is inradius and R

is circumradius.​

Answer 1

Step-by-step explanation:

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

Answer 2

Step-by-step explanation:

$\mathfrak{\huge{\pink{\underline{\underline{Answer :}}}}}$

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

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