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 $AB + CD = AD + BC$.

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

Prove that the parallelogram circumscribing a circle is a rhombus.

$A$ triangle $ABC$ is drawn to circumscribe a circle of radius $4 \, cm$ such that the segments $BD$ and $DC$ into which $BC$ is divided by the point of contact $D$ are of lengths $8 \, cm$ and $6 \, cm$ respectively (see figure). Find the sides $AB$ and $AC$ (in $cm$).

How many tangents can a circle have?