In the given figure, PB is a tangent to the circle with centre O at B . AB is a chord of the circle of length 24 cm…

CBSE Class 10 Maths PYQ · Circles · Triangle & Circle · 3 Marks · March 2025 · Standard

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983 Marks · March 2025 · Standard
In the given figure, $PB$ is a tangent to the circle with centre $O$ at $B$. $AB$ is a chord of the circle of length $24$ cm and at a distance of $5$ cm from the centre of the circle. If the length $PB$ of the tangent is $20$ cm, find the length of $OP$.
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Sol.
Join $OB$
$AB = 24$ cm, $OM = 5$ cm, $PB = 20$ cm
$AM = MB = 12$ cm
In $\triangle OMB$, $OB = \sqrt{5^2 + 12^2} = 13$ cm
As $PB$ is tangent $\Rightarrow PB \perp OB\\$ In rt $\triangle OBP$, $OP = \sqrt{13^2 + 20^2} = \sqrt{569}$ cm
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