From a point $Q$,the length of the tangent to a circle is $24 \, cm$ and the distance of $Q$ from the centre is $25 \, cm$. The radius of the circle is (in $cm$)

$A$ quadrilateral $ABCD$ is drawn to circumscribe a circle (see figure). Prove that $AB + CD = AD + BC$.

$PQ$ is a chord of length $8 \, cm$ of a circle of radius $5 \, cm$. The tangents at $P$ and $Q$ intersect at a point $T$ (see figure). Find the length $TP$.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Prove that in two concentric circles,the chord of the larger circle,which touches the smaller circle,is bisected at the point of contact.