In $\triangle ABC$,$m \angle B = 90^\circ$,$AB = 4$ and $BC = 3$. Find the radius of the incircle of the triangle.

If $\square ABCD$ is a cyclic quadrilateral and also a rectangle,and if $AB = 5$ and $BC = 12$,then $AC = \ldots$

Two concentric circles having radii $41$ and $40$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.

$\odot(P, 3)$ and $\odot(P, 5)$ are two concentric circles. Chord $\overline{AB}$ of $\odot(P, 5)$ touches $\odot(P, 3)$ at $M$. Find $AB$.

Which of the following groups correctly matches the data of Part $I$ with the data of Part $II$?

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 $= 6$

$P$ is a point in the exterior of $\odot(O, r)$ and the tangents from $P$ to the circle touch the circle at $X$ and $Y$. Find $m\angle XOP$,if $m\angle XPO = 65^\circ$. (in $^\circ$)