[Theorem on the lengths of a tangent and a secant; the product of the entire secant and its external part [Tangent lines and touching circles

A circle passing through the vertex $P$ of triangle $P Q R$ touches the side $Q R$ at point $F$ and intersects sides $P Q$ and $P R$ at points $M$ and $N$, respectively, different from vertex $P$. Find the ratio $Q F: F R$, given that the length of side $P Q$ is one and a half times the length of side $P R$, and the ratio $Q M: R N=1: 6$.

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Apply the Tangent-Secant Theorem.

## Answer

$1: 2$.