Given, OA=1 unit, OB=13 unit Since, OB is diameter of circle. Then, radius(r)=13∕2=6.5 units
Draw a line joining points P and C, where C is the centre of the given circle. Then, PC= radius of circle =6.5 units OC= radius of circle =6.5 units Now, AC=OC−OA=6.5−1=5.5 unit Then, using Pythagoras theorem, (PA)2‌‌=(PC)2−(AC)2 ‌‌=(6.5)2−(5.5)2 ‌‌=(6.5−5.5)(6.5+5.5) ‌‌=(1)(12)=12 ∴‌‌PA‌‌=√12 ‌ Then, ‌PQ‌‌=2PA=2√12 ‌ Hence, area of ‌△PQB=‌
1
2
×‌ Base ‌×(‌ Height ‌) ‌‌=‌
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2
×(PQ)×(AB) ‌‌=‌
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×(PQ)×(OB−OA) ‌‌=‌
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×(2√12)×(13−1) ‌‌=12√12=24√3‌ sq units ‌