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In the given figure, PQRS is a quadrilateral such that $\angle S = 90^{\circ}$. A circle with centre 'O' is inscribed in the quadrilateral. The circle touches PQ, QR, RS and SP at points M, N, T and L respectively. If MQ = 19 cm, RQ = 30 cm and SR = 21 cm, then find the radius of the circle.
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NQ = MQ = 19
$\therefore$ RN = $30 - 19 = 11$ cm
$\therefore$ RT = 11 cm
$\therefore$ TS = $21 - 11 = 10$ cm
Since SLOT is a square
Therefore radius of the circle = TS = 10 cm
$\therefore$ RN = $30 - 19 = 11$ cm
$\therefore$ RT = 11 cm
$\therefore$ TS = $21 - 11 = 10$ cm
Since SLOT is a square
Therefore radius of the circle = TS = 10 cm