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Question-8916




Question Number 8916 by kuldeep singh raj last updated on 05/Nov/16
Commented by Rasheed Soomro last updated on 05/Nov/16
Is O the centre of the circle?
$$\mathrm{Is}\:\mathrm{O}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}? \\ $$
Commented by kuldeep singh raj last updated on 05/Nov/16
yes
$$\mathrm{yes} \\ $$
Answered by sandy_suhendra last updated on 05/Nov/16
let ∠OAB=∠OBA=α  so ∠AOB=180−2α  ∠ACB=(1/2)∠AOB=90−α  ∠DBC=180−90−∠ACB                =90−(90−α)=α=∠OAB
$$\mathrm{let}\:\angle\mathrm{OAB}=\angle\mathrm{OBA}=\alpha \\ $$$$\mathrm{so}\:\angle\mathrm{AOB}=\mathrm{180}−\mathrm{2}\alpha \\ $$$$\angle\mathrm{ACB}=\frac{\mathrm{1}}{\mathrm{2}}\angle\mathrm{AOB}=\mathrm{90}−\alpha \\ $$$$\angle\mathrm{DBC}=\mathrm{180}−\mathrm{90}−\angle\mathrm{ACB} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{90}−\left(\mathrm{90}−\alpha\right)=\alpha=\angle\mathrm{OAB} \\ $$
Commented by kuldeep singh raj last updated on 06/Nov/16
thanxsir
$$\mathrm{thanxsir} \\ $$

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