In a Delta ABC, if angle C = 90^{circ}, r and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) In a right-angled triangle $\Delta ABC$ with $\angle C = 90^{\circ}$, the inradius $r$ is given by $r = \frac{a+b-c}{2}$.Since $\angle C = 90^{\ci

Vedclass · Accepted Answer

$a+b$

Vedclass · Answer

(C) In a right-angled triangle $\Delta ABC$ with $\angle C = 90^{\circ}$, the inradius $r$ is given by $r = \frac{a+b-c}{2}$.Since $\angle C = 90^{\circ}$, the hypotenuse $c$ is the diameter of the circumcircle, so the circumradius $R = \frac{c}{2}$, which implies $2R = c$.Now, consider the expression $2(r+R) = 2r + 2R$.Substituting the values, we get $2(\frac{a+b-c}{2}) + c$.$= (a+b-c) + c = a+b$.Therefore, $2(r+R) = a+b$.

In a $\Delta ABC$, if $\angle C = 90^{\circ}$, $r$ and $R$ are the inradius and circumradius of the $\Delta ABC$ respectively, then $2(r+R)$ is equal to

Similar Questions

The area of the equilateral triangle which contains three coins of unit radius is

In a triangle $ABC$,if $r_1=3, r_2=4, r_3=6$,then $b=$

In an equilateral triangle $ABC$, the ratio $r : R : r_1$ is

In $\Delta ABC,$ if $b = 6, c = 8$ and $\angle A = 90^\circ,$ then the circumradius $R$ is:

In an equilateral triangle,the inradius $(r)$ and the circumradius $(R)$ are connected by which of the following relations?

Vedclass Test Series

Exam Paper Generator

Online Exam Module