The radius of the incircle of a triangle PQR | vedclass

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(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

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$1$

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(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:

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