**Given:**
<XOY is a given angle which has to be trisected.

**Construction:**
Draw a circle "O" intersecting OX and OY at A and B respectively.

Joi A, B. Draw a semi circle on AB, AB diameter and P center.

Divide the semi circle at C, D such that arc AC = arc CD = arc DB = radius AP

Join O,C and O,D. OC and OD intersect arc AB at E and F.

**Proof:**
OA = OE = OF = OB (radii of circle O)

arc AB and semi circle are standing on the same straight line AB.

Further arc AC = arc CD = arc DB (construction)

Hence

Arc AE = arc EF = arc FB (experimental conclusion)

I'm not familiar with "experimental conclusion" as a reason in a geometric proof ... ???
These arcs subtant <AOE, <EOF, <FOB which are equal as equal arcs subtant equal angles at the centre

Therefore <AOE = <EOF = <FOB

Hence the trisection

Solved by:

Mohd Shafiuddin Ahmed

Retired Headmaster

Ganapavaram - village & post

Kodad mandal - Nalagonda District

Andhra Pradesh, India - PIN - 508206