AB is a chord of the circle $$x2+y2=25$$. The tangents to the circle at A and B intersect at C . If (2$$,$$3) is the midpoint of AB, then the area of quadrilateral OACB (Where$$ O is $$origin) is

Question

AB is a chord of the circle $$x2+y2=25$$. The tangents to the circle at A and B intersect  at C . If (2$$,$$3) is the midpoint of AB, then the area of quadrilateral OACB (Where$$ O is  $$origin) is

Infinity Learn · Accepted Answer

Here $$OB=OA=5$$ $$($$ radius of $$circle)$$ $$OP=(2$$−$$0)2+(3$$−$$0)2=13$$ Let ∠$$OBP=$$θ, then ∠$$PCB=$$θ From ΔOPB,$$cos$$⁡$$(90$$−θ$$)=OPOB=135$$⇒$$sin$$⁡θ$$=135$$⇒$$cot$$⁡θ$$=2313$$ Area of quadrilateral $$OACB=2$$×$$12$$×OB×BC From ΔOBC,$$cot$$⁡θ$$=BCOB=BC5$$∴ Area of quadrilateral $$OACB=5$$×$$5cot$$⁡θ$$=25$$×$$2313=50313$$ sq.units

$A B is a chord of the circle x^{2} + y^{2} = 25 . The tangents to the circle at A and B intersect$ $at C . If (2, 3) is the midpoint of A B, then the area of quadrilateral O A C B (Where O is$ $origin) is$

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AB is a chord of the circle x2+y2=25. The tangents to the circle at A and B intersect at C . If (2,3) is the midpoint of AB, then the area of quadrilateral OACB (Where O is origin) is

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$A B is a chord of the circle x^{2} + y^{2} = 25 . The tangents to the circle at A and B intersect$ $at C . If (2, 3) is the midpoint of A B, then the area of quadrilateral O A C B (Where O is$ $origin) is$