(B) $O$ is the centre of the circle and $P$ is the point of contact of the tangent.Since the radius is always perpendicular to the tangent at the poin

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(B) $O$ is the centre of the circle and $P$ is the point of contact of the tangent.Since the radius is always perpendicular to the tangent at the point of contact,$\angle OPQ = 90^\circ$.Given: $OP = 7 \, cm$ (radius) and $PQ = 24 \, cm$.In right-angled $\Delta OPQ$,by Pythagoras theorem:$OQ^2 = OP^2 + PQ^2$$OQ^2 = (7)^2 + (24)^2$$OQ^2 = 49 + 576$$OQ^2 = 625$$OQ = \sqrt{625} = 25 \, cm$.

Class 10 Mathematics Circles Mix Examples - Circles

Medium

$A$ line drawn from the centre $O$ of a circle with radius $7 \, cm$ intersects the tangent at point $P$ on the circle at point $Q$,such that $PQ = 24 \, cm$. Find $OQ$.

A
$12$
B
$25$
C
$28$
D
$32$

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Medium

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Write 'True' or 'False' and give reasons for your answer.
The length of the tangent from an external point $P$ on a circle with centre $O$ is always less than $OP$.

Medium

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$A$ line drawn from the centre $O$ of a circle with radius $7 \, cm$ intersects the tangent at point $P$ on the circle at point $Q$,such that $PQ = 24 \, cm$. Find $OQ$.

Similar Questions

$A$ tangent $\overline{PM}$ is drawn from a point $P$ outside $\odot(O, 8)$. $\overline{OP}$ intersects the circle at $N$. If $NP = 2$,then $PM = \ldots$

Write 'True' or 'False' and give reasons for your answer.The length of the tangent from an external point $P$ on a circle with centre $O$ is always less than $OP$.

$\overline{AB}$ is a chord of $\odot(O, 13)$ such that $AB = 24$. Tangents at $A$ and $B$ to the circle intersect at $P$. Find $PA$.

In $\triangle ABC$,$m \angle B = 90^\circ$,$AB = 4$ and $BC = 3$. Find the radius of the incircle of the triangle.

Two concentric circles having radii $17$ and $8$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.

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Write 'True' or 'False' and give reasons for your answer.
The length of the tangent from an external point $P$ on a circle with centre $O$ is always less than $OP$.