`alpha,beta and gamma` are parametric angles of three points P, Q and R respectively, on the circle `x^2 + y^2 = 1` and A is the point (-1, 0). If the lengths of the chords AP, AQ and AR are in GP, then `cos alpha/2, cos beta/2 and cos gamma/2` are in

Options

A. AP
B. GP
C. HP
D. none of these

Answer

B

Explanation

Let `P(cos alpha, sin alpha), Q (cos beta, sin beta) ` and `R(cos lambda, sin lambda)` be three specified points on the given circle. T
Then,
`AP=sqrt((-1-cos alpha)^(2)+(0-sin alpha)^(2))`
`rArr AP=sqrt(2+2cos alpha)=sqrt(4 cos^(2) alpha//2)=2 cos alpha//2`
Similarly, we have
`AQ=2 cos beta//2` and `AR=2 cos lambda//2`
Now,
AP, AQ, AR are in GP
`rArr 2 cos alpha//2, 2 cos beta//2, 2cos lambda//2` are in GP
`rArr cos alpha//2, cos beta//2, cos lambda//2` are in GP.