Problem 716. Intersecting Circles, Center, Radius, Perpendicular, 90 Degrees. Level: High School, College, SAT Prep.

In the figure below, the circles O and O' intersect at A and B. C is a point on circle O, AC and BC meet circle O' at D and E, respectively. F is a point on circle O', AF and BF meet circle O at H and G, respectively. OC and O'F meet at L, CO meets HG at C', FO' meets DE at F', HG and DE meet at M. Prove that ML is perpendicular to C'F'.

 

FACTS AND HINTS:

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."