If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

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Solution

As given,
Here,
$P Q = 24 c m$
$O Q = 25 c m$
we know that $P Q ⊥ O P$
therefore from pythagoras theorem,
$O Q^{2} = O P^{2} + P Q^{2}$
$25^{2} = r^{2} + 24^{2}$
$r = \sqrt{25^{2} - 24^{2}}$
$r = 7 c m$

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If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

As given,Here, PQ=24 cmOQ=25 cmwe know that PQ⊥OPtherefore from pythagoras theorem,OQ2=OP2+PQ2252=r2+242r=√252−242r=7 cm

As given,
Here,
$P Q = 24 c m$
$O Q = 25 c m$
we know that $P Q ⊥ O P$
therefore from pythagoras theorem,
$O Q^{2} = O P^{2} + P Q^{2}$
$25^{2} = r^{2} + 24^{2}$
$r = \sqrt{25^{2} - 24^{2}}$
$r = 7 c m$