EHF is tangent to the purple circle at E, and EN is tangent to the red circle at N. A and C are the circle centers. A blue rectangle has three corners HEC and the point A on one side. What is the ratio of areas, green square to orange quadrilateral?

Solution

Green : orange is 2 : 1.

B is the centre of dilation between the two circles, which gives that EBI is a straight line directly. I had to draw a picture for the rest, it’s just two similar triangles, as well as power of a point for t² = ab.

EHF is tangent to the purple circle at E, and EN is tangent to the red circle at N. A and C are the circle centers. A blue rectangle has three corners HEC and the point A on one side. Ratio of areas green square to orange quadrilateral? https://t.co/WpF4ENhOtr By @MarshallWBuck pic.twitter.com/21xCXmtLM9

— Mirangu (@Mirangu1) August 6, 2024