The blue unit circle has a diameter and several colored chords. The red chord bisects the angle between the green chords. Express the sum of the green chords in terms of the red and purple chords.

Solution

Green=red*purple.

Apply Ptolemy’s theorem to DFBE: g1*BE+g2*BF=r*FE g1+g2=r*FE / BE=r*2*GE/BE=r*2*b/2=r*b.

The blue unit circle has a diameter and several colored chords. The red chord bisects the angle between the green chords. Express the sum of the green chords in terms of the red and purple chords. https://t.co/DdeXC5nEVI By @MarshallWBuck pic.twitter.com/EEBKCAlepy

— Mirangu (@Mirangu1) August 20, 2024