Question

In the figure above, find the length of segment $AB$ given that the two lines are tangent to the circle of radius $2$ at points $A$ and $B$.

• A. $1,37$
• B. $1.69$
• C. $3.06$
• D. $3.63$
• E. $4$

Answer 1

The correct option is D $3.63$

WKT $AC=BC$

$OA=OB=r$

$OC$ is common

$OC$ is angular bisector of $\angle ACB$

$OC\perp AB$

$△DACand△DBC$ are congruent

$AD=BD$

In $△OAC$

$\angle OAC=90$

$\angle ACO=25$

$OA=2$

$\tan 25=\frac{OA}{AC}=\frac{2}{AC}$

$⟹AC=\frac{2}{\tan 25}$

In $△DAC$

$\angle CDA=90$

$\sin 25=\frac{AD}{AC}$

$⟹AC=\sin 25\times \frac{2}{\tan 25}=2\cos 25$

$AB=2AD=4\cos 25=3.63$