Curriculum · Olympiad Topics · Advanced Geometry

Cyclic Quadrilaterals & Angle Hunting

Ptolemy, cyclic characterizations, and the concyclic points nobody mentioned.

Objectives

Prove points concyclic
Apply Ptolemy's theorem
Chase directed angles

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Train the topic

●●●●○Quadrilateral

ABCD

is cyclic with

\angle A = 70°

. What is

\angle C

in degrees?Olympiad training ●●●●●Equilateral triangle

ABC

is inscribed in a circle, and

P

lies on arc

BC

not containing

A

. If

PB = 3

and

PC = 5

, what is

PA

?Olympiad classic