In the given figure, TP and TQ are tangents to a circle with centre M , touching another circle with centre N at A and…
CBSE Class 10 Maths PYQ · Circles · Tangents & All · 5 Marks · March 2026 · Standard
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365 Marks · March 2026 · Standard
In the given figure, $TP$ and $TQ$ are tangents to a circle with centre $M$, touching another circle with centre $N$ at $A$ and $B$ respectively. It is given that $MQ = 13$ cm, $NB = 8$ cm, $BQ = 35$ cm and $TP = 80$ cm. (i) Name the quadrilateral $MQBN$. (ii) Is $MN$ parallel to $PA$? Justify your answer. (iii) Find length $TB$. (iv) Find length $MN$.
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(i) $BN \parallel QM$ and $QB \parallel MN$ The quadrilateral $MQBN$ is a trapezium. (I) (1 Mark) (ii) No, as $AN \neq PM$ (II) (1 Mark) (iii) $TQ = TP = 80$ cm $\therefore TB = 80 - 35 = 45$ cm (III) (1 Mark) Note: If $MNT$ is considered a straight line and similarity of triangles is used to find $TB$ then $TB = 56$ cm may be considered as correct answer. (iv) $MN^2 = NS^2 + MS^2$ $= 35^2 + (13 - 8)^2$ (IV) (1 Mark) $= 1225 + 25$ (V) ($\frac{1}{2}$ Mark) $= 1250$ $\therefore MN = 25\sqrt{2}$ cm (VI) ($\frac{1}{2}$ Mark)
