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Question Number 72414 by aliesam last updated on 28/Oct/19

Commented by aliesam last updated on 28/Oct/19

a,b and d are centres of three circles   find   ((AC)/(AB))

$${a},{b}\:{and}\:{d}\:{are}\:{centres}\:{of}\:{three}\:{circles}\: \\ $$$${find}\: \\ $$$$\frac{{AC}}{{AB}} \\ $$

Answered by mr W last updated on 28/Oct/19

let AC=a, AB=BD=b  a sin 30°=b sin 60°  ((AC)/(AB))=(a/b)=((sin 60°)/(sin 30°))=(√3)

$${let}\:{AC}={a},\:{AB}={BD}={b} \\ $$$${a}\:\mathrm{sin}\:\mathrm{30}°={b}\:\mathrm{sin}\:\mathrm{60}° \\ $$$$\frac{{AC}}{{AB}}=\frac{{a}}{{b}}=\frac{\mathrm{sin}\:\mathrm{60}°}{\mathrm{sin}\:\mathrm{30}°}=\sqrt{\mathrm{3}} \\ $$

Commented by aliesam last updated on 28/Oct/19

god bless you sir

$${god}\:{bless}\:{you}\:{sir} \\ $$

Commented by mr W last updated on 28/Oct/19

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