When we talk about the theorem about tangents from a point outside a circle, we find that two tangents drawn from that point are the same length. Let’s break it down step by step!

1. Setup: Picture a circle with a center called $O$. There’s a point $P$ outside this circle. We draw two tangents, which we will call $PA$ and $PB$. Points $A$ and $B$ are where the tangents touch the circle.

2. Right Angles: One cool fact about tangents is that they make right angles with the radius of the circle. This means the line $OA$ (the radius) makes a right angle with the tangent $PA$. The same goes for $OB$ and $PB$. This makes triangles $OAP$ and $OBP$ right triangles.

3. Using the Pythagorean Theorem: In math, there’s a useful rule called the Pythagorean theorem that we can use here:

   • For triangle $OAP$: $OP^2 = OA^2 + AP^2$
   • For triangle $OBP$: $OP^2 = OB^2 + BP^2$

4. Equality of Radii: Since both triangles share the same length $OP$ and the lengths of $OA$ and $OB$ are equal (because they are both radii of the same circle), we can say that $AP^2$ is equal to $BP^2$.

So, this means that $AP$ (the length of one tangent) is the same as $BP$ (the length of the other tangent).

This shows that the tangents from point $P$ are equal, which is an important concept about circles!