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In the given figure, O is the centre of the circle. PQ and PR are tangents.
Show that the quadrilateral PQOR is cyclic.
Show that the quadrilateral PQOR is cyclic.
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As radius is perpendicular to tangent,
$\angle PQO = 90^\circ$, $\angle PRO = 90^\circ$ (1 Mark)
$\therefore \angle PQO + \angle PRO = 180^\circ$ (1/2 Mark)
One pair of opposite angles is supplementary
$\therefore$ Quadrilateral PQOR is cyclic (1/2 Mark)
$\angle PQO = 90^\circ$, $\angle PRO = 90^\circ$ (1 Mark)
$\therefore \angle PQO + \angle PRO = 180^\circ$ (1/2 Mark)
One pair of opposite angles is supplementary
$\therefore$ Quadrilateral PQOR is cyclic (1/2 Mark)