The radius of the incircle of a triangle PQR | vedclass

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

Question

(D) The vertices of the triangle are $P(0, 0)$,$Q(3, 0)$,and $R(0, 4)$.This is a right-angled triangle with the right angle at $P(0, 0)$.The lengths o

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) The vertices of the triangle are $P(0, 0)$,$Q(3, 0)$,and $R(0, 4)$.This is a right-angled triangle with the right angle at $P(0, 0)$.The lengths of the sides are:$PQ = \sqrt{(3-0)^2 + (0-0)^2} = 3$$PR = \sqrt{(0-0)^2 + (4-0)^2} = 4$$QR = \sqrt{(3-0)^2 + (0-4)^2} = \sqrt{9 + 16} = 5$The radius of the incircle $r$ of a right-angled triangle is given by the formula $r = \frac{a + b - c}{2}$,where $a$ and $b$ are the legs and $c$ is the hypotenuse.Here,$a = 3$,$b = 4$,and $c = 5$.$r = \frac{3 + 4 - 5}{2} = \frac{2}{2} = 1$.

The radius of the incircle of a triangle $PQR$ with vertices $P(0, 0)$,$Q(3, 0)$,and $R(0, 4)$ is:

Similar Questions

In a $\triangle ABC$,if $a: b: c = 4: 5: 6$,then the ratio of the radius of its circumcircle to that of its incircle is:

If $a, b$ and $c$ are the sides of $\triangle ABC$ for which $r_1=8, r_2=12$ and $r_3=24$,then the ordered triad $(a, b, c)=$

In a $\triangle ABC$,if $a=13, b=14, c=15$,then find the value of $r_1$.

If the angular bisector of the angle $A$ of the triangle $ABC$ meets its circumcircle at $E$ and the opposite side $BC$ at $D$,then $DE \cos \frac{A}{2} = $

Let $ABC$ be an equilateral triangle with side length $a$. Let $R$ and $r$ denote the radii of the circumcircle and the incircle of triangle $ABC$ respectively. Then,as a function of $a$,the ratio $\frac{R}{r}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module