Question Number 23679 by math solver last updated on 03/Nov/17
Answered by ajfour last updated on 03/Nov/17
$$\left({B}\right)\:\mathrm{2}:\mathrm{3} \\ $$
Commented by math solver last updated on 03/Nov/17
$$\mathrm{sir}\:\mathrm{plzz}\:\mathrm{provide}\:\mathrm{sol}.\:\mathrm{also}.... \\ $$
Commented by math solver last updated on 04/Nov/17
$$?? \\ $$$$ \\ $$
Answered by mrW1 last updated on 04/Nov/17
$$\angle\mathrm{BAC}=\angle\mathrm{BCA}=\mathrm{15}° \\ $$$$\angle\mathrm{OAC}=\mathrm{60}−\mathrm{15}=\mathrm{45}° \\ $$$$\angle\mathrm{OCA}=\mathrm{45}−\mathrm{15}=\mathrm{30}° \\ $$$$\angle\mathrm{OFA}=\angle\mathrm{OAC}=\mathrm{45}° \\ $$$$\angle\mathrm{OFC}=\mathrm{180}−\mathrm{45}=\mathrm{135}° \\ $$$$\angle\mathrm{COF}=\mathrm{180}−\mathrm{30}−\mathrm{135}=\mathrm{15}° \\ $$$$\angle\mathrm{BOF}=\angle\mathrm{BOC}−\angle\mathrm{COF}=\mathrm{45}−\mathrm{15}=\mathrm{30}° \\ $$$$\frac{\angle\mathrm{BOF}}{\angle\mathrm{BOC}}=\frac{\mathrm{30}}{\mathrm{45}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{answer}\:\left(\mathrm{B}\right) \\ $$