CBSE 2025 · Region 3 · Set 3 · Q27 · 3 marks
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 $\displaystyle 24$ cm and at a distance of $\displaystyle 5$ cm from the centre of the circle. If the length PB of the tangent is $\displaystyle 20$ cm, find the length of OP.
Marking-scheme solution
Join OB
\[\begin{aligned}
& A B=24 \mathrm{~cm}, \mathrm{OM}=5 \mathrm{~cm}, \mathrm{~PB}=20 \mathrm{~cm} \\
& \mathrm{AM}=\mathrm{MB}=12 \mathrm{~cm} \\
& \text { In } \triangle \mathrm{OMB}, \mathrm{OB}=\sqrt{5^{2}+12^{2}}=13 \mathrm{~cm} \\
& \text { As } \mathrm{PB} \text { is tangent } \Rightarrow \mathrm{PB} \perp \mathrm{OB} \\
& \text { In rt } \triangle \mathrm{OBP}, \mathrm{OP}=\sqrt{13^{2}+20^{2}}=\sqrt{569} \mathrm{~cm}
\end{aligned}
\]CirclesLength of Tangents from an External PointApplyshort_answermedium
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