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(D) For a right-angled triangle with sides $a, b$ and hypotenuse $c$,the in-radius $r$ is given by the formula $r = \frac{a+b-c}{2}$.$1.$ For $\Delta

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$(1-b), (2-a), (3-d), (4-c)$

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(D) For a right-angled triangle with sides $a, b$ and hypotenuse $c$,the in-radius $r$ is given by the formula $r = \frac{a+b-c}{2}$.$1.$ For $\Delta ABC$ with sides $3, 4, 5$: $r = \frac{3+4-5}{2} = \frac{2}{2} = 1$. Matches $(b)$.$2.$ For $\Delta PQR$ with sides $5, 12, 13$: $r = \frac{5+12-13}{2} = \frac{4}{2} = 2$. Matches $(a)$.$3.$ For $\Delta XYZ$ with sides $8, 15, 17$: $r = \frac{8+15-17}{2} = \frac{6}{2} = 3$. Matches $(d)$.$4.$ For $\Delta MNP$ with sides $20, 21, 29$: $r = \frac{20+21-29}{2} = \frac{12}{2} = 6$. Matches $(c)$.Thus,the correct matching is $(1-b), (2-a), (3-d), (4-c)$.

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 $= 6$

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