[ Two tangents drawn from one point $]$

Given a circle of radius 1. From an external point $M$, two perpendicular tangents $MA$ and $MB$ are drawn to the circle. Between the points of tangency $A$ and $B$ on the smaller arc $AB$, a point $C$ is taken, and a third tangent $KL$ is drawn through it, forming a triangle $KLM$ with the tangents $MA$ and $MB$. Find the perimeter of this triangle.
Tangents drawn from a single point to a circle are equal to each other.

## Solution

Since $KA = KC$ and $BL = LC$, then

$$
\begin{gathered}
ML + LK + KM = ML + (LC + CK) + KM = \\
= (ML + LC) + (CK + KM) = (ML + LB) + (AK + KM) = \\
= MB + AM = 1 + 1 = 2.
\end{gathered}
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_36c4956010bd91c4b4eeg-14.jpg?height=406&width=426&top_left_y=1509&top_left_x=816)

## Answer

2.