Two circles each of which passes through the centre of the other intersect points M and N.

Question

Two circles each of which passes through the centre of the other intersect points M and N. A line from M intersects the circle at K and L as shown in the figure. If KL = 6 compute the area of ∆KLN.

I was attempting a Practice Paper and stumbled on this Question.

I think the tangent secant theorem must used somewhere which states that.

$Tangent^2=Outer Secant×Whole Secant$

But I don't know where to apply it so I am clueless.

I don't know where to start from.

Any help will be appreciated

Answer 1

Realize that $\angle NKM= 120^o$ and that $\angle KLN= 60^o$, which leaves $\Delta KLN$ an equilateral triangle. The answer is therefore $9\sqrt{3}$.