Overview

Advanced geometry blends similarity, power of a point, and homothety. Draw accurate diagrams and track equal angles carefully.

Key Ideas

• Ceva's theorem: for concurrent cevians, $\frac{AF}{FB}\cdot\frac{BD}{DC}\cdot\frac{CE}{EA}=1$.
• Homothety maps circles to circles and preserves tangency.
• Power of a point applies to tangents and secants.

Worked Example

If two tangents from $P$ touch a circle at $A$ and $B$, then $PA=PB$. This follows from equal tangents to a circle.

Practice Problems