CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
From an external point P, a tangent PT has been drawn to a circle with centre O and radius 3 cm (touching it at Q), intersecting its concentric circle at A and B. If $AB = 8$ cm and $OA = AP$, the length PQ equals
A. $8$ cm
B. $10$ cm
C. $9$ cm
D. $12$ cm
✅ Answer & Solution
✅ Correct Answer: C
Step 1: $OQ\perp AB$ (radius $\perp$ tangent at the point of contact Q), and $OQ=3$ cm.
Step 2: A perpendicular from the centre bisects the chord AB of the bigger circle, so
$$AQ=QB=\frac{AB}{2}=\frac{8}{2}=4\text{ cm}$$
Step 3: In right $\triangle OQA$, by Pythagoras theorem:
$$OA=\sqrt{OQ^2+AQ^2}=\sqrt{3^2+4^2}=\sqrt{25}=5\text{ cm}$$
Step 4: Given $OA=AP$, so $AP=5$ cm.
Step 5: $PQ=AQ+AP=4+5=9$ cm.
Answer: (C) $9$ cm
