It has been almost 10 months since I sat for bdmo 2023’s national. And couldn’t solve this geometry problem yet.Here is it-

Let the points 𝑨, 𝑩,𝑪 lie on a line in this order. 𝑨𝑩 is the diameter of semicircle 𝝎𝟏, 𝑨𝑪 is the

diameter of semicircle 𝝎𝟐. Assume both 𝝎𝟏 and 𝝎𝟐 are on the same side of 𝑨𝑪. 𝑫 is a point on 𝝎𝟐

such that 𝑩𝑫 ⊥ 𝑨𝑪. A circle centered at 𝑩 with radius 𝑩𝑫 intersects 𝝎𝟏 at 𝑬. 𝑭 is on 𝑨𝑪 such that

𝑬𝑭 ⊥ 𝑨𝑪. Prove that 𝑩𝑪 = 𝑩𝑭.

Is there anyone to help?