In the figure,if TP and TQ are the two tangen | vedclass

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(B) It is given that $TP$ and $TQ$ are tangents to the circle from an external point $T$.The radius of a circle is perpendicular to the tangent at the

Vedclass · Accepted Answer

$70$

Vedclass · Answer

(B) It is given that $TP$ and $TQ$ are tangents to the circle from an external point $T$.The radius of a circle is perpendicular to the tangent at the point of contact.Therefore,$OP \perp TP$ and $OQ \perp TQ$.This implies $\angle OPT = 90^{\circ}$ and $\angle OQT = 90^{\circ}$.In the quadrilateral $POQT$,the sum of all interior angles is $360^{\circ}$.$\angle OPT + \angle POQ + \angle OQT + \angle PTQ = 360^{\circ}$Substituting the known values:$90^{\circ} + 110^{\circ} + 90^{\circ} + \angle PTQ = 360^{\circ}$$290^{\circ} + \angle PTQ = 360^{\circ}$$\angle PTQ = 360^{\circ} - 290^{\circ} = 70^{\circ}$

In the figure,if $TP$ and $TQ$ are the two tangents to a circle with centre $O$ such that $\angle POQ = 110^{\circ}$,then $\angle PTQ$ is equal to: (in $^{\circ}$)

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