α, β and y are the parametric angles of three points P, Q, and R respectively, on the circle $$x2$$ $$+$$ $$y2$$ $$=$$ $$1$$, and A is the point $$(-1$$, $$0)$$. If the lengths of the chords AP, AQ and AR are in GP, then $$cos$$ α$$/2$$, $$cos$$ β$$/2$$ and $$cos$$ γ$$/2$$ are in

Question

α, β and y are the parametric angles of three points P, Q, and R respectively, on the circle $$x2$$ $$+$$ $$y2$$ $$=$$ $$1$$, and A is the point $$(-1$$, $$0)$$. If the lengths of the chords AP, AQ and AR are in GP, then $$cos$$ α$$/2$$, $$cos$$ β$$/2$$ and $$cos$$ γ$$/2$$ are in

Infinity Learn · Accepted Answer

Let P $$($$$$cos$$ α, $$sin$$α$$)$$, Q $$($$$$cos$$ β, $$sin$$ β$$)$$ and R $$($$$$cos$$γ, $$sin$$ γ$$)$$ be three specified points on the given circle. Then,              $$AP=($$−$$1$$−$$cos$$⁡α$$)2+(0$$−$$sin$$⁡α$$)2$$⇒ $$AP=2+2cos$$⁡α$$=4cos2$$⁡α$$/2=2cos$$⁡α$$/2Similarly$$, we have     $$AQ=2cos$$⁡β$$/2$$ and $$AR=2cos$$⁡γ$$/2Now$$,      AP, AQ, AR are in GP⇒ $$2cos$$⁡α$$/2$$,$$2cos$$⁡β$$/2$$,$$2cos$$⁡γ$$/2$$ are in GP⇒ $$cos$$⁡α$$/2$$,$$cos$$⁡β$$/2$$,$$cos$$⁡γ$$/2$$ are in GP.

$α, β$ and y are the 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 $A P, A Q$ and $A R$ are in $G P,$ then $\cos α / 2, \cos β / 2$ and $\cos γ / 2$ are in

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α, β and y are the parametric angles of three points P, Q, and R respectively, on the circle x2 + y2 = 1, and A is the point (-1, 0). If the lengths of the chords AP, AQ and AR are in GP, then cos α/2, cos β/2 and cos γ/2 are in

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$α, β$ and y are the 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 $A P, A Q$ and $A R$ are in $G P,$ then $\cos α / 2, \cos β / 2$ and $\cos γ / 2$ are in