Q.
The angle between the chords of the circle x2+y2=100, which passes through the point (7,1) and also divides the circumference of the circle into two arcs whose lengths are in the ratio 2:1, is equal to
1707
219
NTA AbhyasNTA Abhyas 2020Conic Sections
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Solution:
Let the chord is AB which subtends an angle θ at the centre (0,0) ⇒θ+2θ=360o ⇒θ=120o=∠AOB
Let the distance of O from AB=h
Then, cos60o=10h=21⇒h=5
Let the equation of the chord is x−7y−1=m ⇒mx−y+1−7m=0 whose distance from (0,0) is equal to 5 ⇒∣∣1+m20−0+1−7m∣∣=5 ⇒1−14m+49m2=25+25m2 ⇒24m2−14m−24=0⇒m1m2=−1 ⇒ Chords are perpendicular