If ABC is an isosceles triangle with base BC, | vedclass

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

Question

(D) Given $r = \frac{\Delta}{s}$ and $r_1 = \frac{\Delta}{s-a}$.$rr_1 = \frac{\Delta^2}{s(s-a)} = \frac{s(s-a)(s-b)(s-c)}{s(s-a)} = (s-b)(s-c)$.Since

Vedclass · Accepted Answer

$R^2 \sin^2 A$

Vedclass · Answer

(D) Given $r = \frac{\Delta}{s}$ and $r_1 = \frac{\Delta}{s-a}$.$rr_1 = \frac{\Delta^2}{s(s-a)} = \frac{s(s-a)(s-b)(s-c)}{s(s-a)} = (s-b)(s-c)$.Since the triangle is isosceles with base $BC$,we have $b = c$.Thus,$rr_1 = (s-b)^2$.Since $2s = a+b+c = a+2b$,we have $s-b = \frac{a+2b-2b}{2} = \frac{a}{2}$.Therefore,$rr_1 = (\frac{a}{2})^2 = \frac{a^2}{4}$.Using the sine rule,$a = 2R \sin A$,so $rr_1 = \frac{(2R \sin A)^2}{4} = \frac{4R^2 \sin^2 A}{4} = R^2 \sin^2 A$.

If $ABC$ is an isosceles triangle with base $BC$,then $rr_1=$

Similar Questions

In $\triangle ABC$,the circle that touches the side $BC$ internally and the other two sides $AB$ and $AC$ externally is called:

If the roots of the equation $x^3-11x^2+36x-36=0$ are the ex-radii of a triangle $ABC$, then the perimeter of the triangle $ABC$ is

If $d_1, d_2, d_3$ are the diameters of three ex-circles of a $\triangle ABC$,then $d_1 d_2 + d_2 d_3 + d_3 d_1 =$

$ABC$ is an isosceles triangle with an inscribed circle with center $O$. Let $P$ be the midpoint of $BC$. If $AB = AC = 15$ and $BC = 10$, then $OP$ equals

In $\triangle ABC$, find the value of $r_1+r_2+r_3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module