<prompt> Acute-angled pembetatu ABC imeandikwa katika mduara na katikati katika O; stackrel frown AB 120circ na stackrel frown BC 72circ.Pointi E inachukuliwa katika safu ndogo AC kiasi kwamba OE ni sawa na AC. Halafu uwiano wa ukubwa wa angle OBE na angle BAC ni:textbfA frac518qquad textbfB frac29qquad textbfC frac1 4qquad textbfD frac13qquad textbfE frac49  <response>: asy choramduara0,0,1; nukta -1,0; jozi A-1,0,B0.5,0.866,C0.978,-0.208,O0,0,E-0.105,-0.995; leboA,-1,0,W; nukta 0.5,0.866; leboB,0.5,0.866,NE; nukta 0.978,-0.208; leboC,0.978,-0.208,SE; nukta 0,0; leboO,0,0,NE; nukta E; leboE,E,S; choraA--B--C--A; kuchoraE--O; asyKwa sababu stackrel frown AB 120circ na stackrel frown BC 72circ, stackrel frown AC 168circ. Pia, OA OC na OE perp AC, hivyo angle AOE angle COE 84circ. Kwa kuwa angle BOC 72circ, angle BOE 156circ. Hatimaye, pembetatu BOE ni pembetatu ya isosceles, hivyo angle OBE 12circ. Kwa sababu angle BAC frac12 cdot 72 36circ, uwiano wa ukubwa wa angle OBE na angle BAC ni frac1236 frac13. 