From an external point $M$, two tangents $MA$ and $MB$ are drawn to a circle of radius 6 cm. If the angle between the tangents is $90^\circ$, find the distance of point $M$ from the center of the circle.

Question

Accepted Answer

6 $\sqrt{2}$ cm. The angle between tangents is $90^\circ$, so the line from the center to $M$ bisects it, making each angle $45^\circ$. In right triangle $OAM$, $OA=6$ cm and $\angle OMA=45^\circ$. Thus $\sin 45^\circ=\frac{OA}{OM}=\frac{6}{OM}$, giving $OM=6\sqrt{2}$ cm.

From an external point $M$, two tangents $MA$ and $MB$ are drawn to a circle of radius 6 cm. If the angle between the tangents is $90^\circ$, find the distance of point $M$ from the center of the circle.

Solution

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