In △ ABC, bisectors of ∠ ABC and ∠ ACB intersect at point O, passing through point o as EF ‖ BC, AB at point E, AC at F, passing through point o as OD ⊥ AC at D, if od = 1cm , AE + AF = 7cm, calculate the area of △ AEF

In △ ABC, bisectors of ∠ ABC and ∠ ACB intersect at point O, passing through point o as EF ‖ BC, AB at point E, AC at F, passing through point o as OD ⊥ AC at D, if od = 1cm , AE + AF = 7cm, calculate the area of △ AEF

Draw your own picture. The intersection of the two bisectors is the inscribed center of the triad. Od is the radius of the inscribed circle
Make the vertical line of AB through O, the perpendicular foot is g, og is also the radius of inscribed circle, OD = og = 1, and then connect OA
At this point, we can see
S triangle AEF = s triangle AEO + s triangle AFO = AE * og / 2 + af * od / 2 = AE * od / 2 + af * od / 2 = (AE + AF) / 2 = 7 / 2