Question

Let BC be the chord of contact of the tangents from a point A to the circle x² + y² = 1.P is any point on the arc BC. Let PX, PY, PZ be the lengths of perpendiculars from P on the AB, BC and CA respectively then PX, PY, PZ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (B)

G.P.

Answer 2

Let A be (0, a) Ž equation of BC is ay = 1

Ž B and C are $\left( \frac{- \sqrt{\alpha^{2} - 1}}{\alpha},\frac{1}{\alpha} \right)$

and $\left( \frac{\sqrt{\alpha^{2} - 1}}{\alpha},\frac{1}{\alpha} \right)$

Ž Equation of AC and BC are

$\frac{- \sqrt{\alpha^{2} - 1}}{\alpha}$x +$\frac{y}{\alpha}$= 1 and $\frac{\sqrt{\alpha^{2} - 1}}{\alpha}$x + $\frac{y}{\alpha}$= 1

and PZ = $\left| \cos\theta\frac{\sqrt{\alpha^{2} - 1}}{\alpha} + \frac{\sin\theta}{\alpha} - 1 \right|$where P ŗ (sin q, cos q)

Ž PY² = PX. PZ