In the following figure,find the radius of th | vedclass

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(A) Let the radius of the circle be $r$. The circle is the incircle of the right-angled triangle $ABC$,where $AB = 3$ and $BC = 4$.Using the Pythagore

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(A) Let the radius of the circle be $r$. The circle is the incircle of the right-angled triangle $ABC$,where $AB = 3$ and $BC = 4$.Using the Pythagorean theorem,the hypotenuse $AC = \sqrt{AB^2 + BC^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.The radius $r$ of the incircle of a right-angled triangle is given by the formula $r = \frac{AB + BC - AC}{2}$.Substituting the values,$r = \frac{3 + 4 - 5}{2} = \frac{2}{2} = 1$.Thus,the radius of the circle is $1$.

Part $I$	Part $II$
$1.$ In $\Delta ABC, AB=3, BC=4, AC=5$	$a.$ In-radius $= 1$
$2.$ In $\Delta PQR, PQ=5, QR=12, PR=13$	$b.$ In-radius $= 2$
$3.$ In $\Delta XYZ, XY=8, YZ=15, XZ=17$	$c.$ In-radius $= 3$
$4.$ In $\Delta MNP, MN=20, NP=21, MP=29$	$d.$ In-radius $= 6$

In the following figure,find the radius of the circle.

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