Revolving chord
P(12,34) is a point in a circle centred at O(0,0) with radius 567. Now a moving line L which passes through P intersect the circle at A and B, M is the mid-point of chord AB. As L rotates about P, the locus (i.e. trace) of point M form a closed curve D.
Find the area of region enclosed by D. (take pi=3.14)
The answer is 1020.5.
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1 solution
Consider that OM⊥AB (line joining centre and mid-point is perpendicular to chord) i.e. ∠PMO=90°, as both P and O are fixed points, M must lie on the circle having PO as diameter. Hence, D is a circle with radius PO/2=√(12^2+34^2 )/2=√325
Thus, the required area = (√325)^2 π=325×3.14=1020.5