If the measure of the angle between two radii | vedclass

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(C) Let the center of the circle be $O$ and the two radii be $OA$ and $OB$. The angle between the radii is $\angle AOB = 48^{\circ}$.Tangents are draw

Vedclass · Accepted Answer

$132$

Vedclass · Answer

(C) Let the center of the circle be $O$ and the two radii be $OA$ and $OB$. The angle between the radii is $\angle AOB = 48^{\circ}$.Tangents are drawn at points $A$ and $B$. Let these tangents meet at point $P$.Since the tangent at any point of a circle is perpendicular to the radius through the point of contact,we have $\angle OAP = 90^{\circ}$ and $\angle OBP = 90^{\circ}$.In the quadrilateral $OAPB$,the sum of the interior angles is $360^{\circ}$.Therefore,$\angle AOB + \angle OAP + \angle OBP + \angle APB = 360^{\circ}$.Substituting the known values: $48^{\circ} + 90^{\circ} + 90^{\circ} + \angle APB = 360^{\circ}$.$228^{\circ} + \angle APB = 360^{\circ}$.$\angle APB = 360^{\circ} - 228^{\circ} = 132^{\circ}$.Thus,the angle between the tangents is $132^{\circ}$.

If the measure of the angle between two radii of the circle is $48^{\circ}$,then the measure of the angle between the tangents drawn at the end points of the radii is $\ldots \ldots \ldots$ (in $^{\circ}$)

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