Prove $R=\sqrt{AP\cdot AQ}$.
Prove $C = \sqrt{AB}$.
Prove $PC = \sqrt{ PA \cdot PB }$.
Given a regular decagon. Prove $a^2+b^2=3R^2$ and $R = \sqrt{ab} = b-a$.
Prove $PC = \sqrt{PA\cdot PB}$.
The green shapes are squares. Prove the radius of the red circle is the geometric mean of the radii of the blue circles.
Prove $c^2 = 4ab$.
Sides of the blue and green triangles are parallel. Prove the area of the red triangle is the geometric mean of the areas of the blue and grren triangles.
Prove $OC = \sqrt{OA\cdot OB}$.
Given $PC = \sqrt{PA\cdot PB}$. Prove $\displaystyle QC = \sqrt{QA'\cdot QB'}$.
The yellow triangle is isosceles. Prove $PC = \sqrt{PA\cdot PB}$.
Prove $c = \sqrt{PA\cdot PB}$.
Prove $r = \sqrt{ab}$.
Prove $OC = \sqrt{ OA\cdot OB }$.
Prove $c = \sqrt{ab}$.
Prove $PC = \sqrt{ PA\cdot PB }$.