Question

Circle in 1st quadrant touches both the axes at A & B. If length of perpendicular from $P(α, β)$ on circle to chord AB is equal to 11. Find $α.β$

Answer 1

C : (x - r)2 + (y-r)2 = r2;
α2 + β2 - 2r(α + β) + r2 = 0

α2 + β2 - 2r(11$\sqrt{2}$ + r) + r2 = 0
α2 + β2 - 22$\sqrt{2}$r - r2 = 0
PF = $\frac{α+β-r}{\sqrt{2}}$ = 11
α + B = 11$\sqrt{2}$ + r
α2 + β2 + 2αβ = 242 + r2 + 22r$\sqrt{2}$
αβ = 121

So, the answer is 121.