It has been almost 10 months since I sat for bdmo 2023βs national. And couldnβt solve this geometry problem yet.Here is it-

Let the points π¨, π©,πͺ lie on a line in this order. π¨π© is the diameter of semicircle ππ, π¨πͺ is the

diameter of semicircle ππ. Assume both ππ and ππ are on the same side of π¨πͺ. π« is a point on ππ

such that π©π« β₯ π¨πͺ. A circle centered at π© with radius π©π« intersects ππ at π¬. π is on π¨πͺ such that

π¬π β₯ π¨πͺ. Prove that π©πͺ = π©π.

Is there anyone to help?