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If PA and PB are two tangents from external point P to a circle with centre O and [tex]angle[/tex]APB = 35 , find the angle OAB.

Answer» In\ \Delta OAP, \angle OAP=90^0\ (PA\ is\ tangent)\\similarly,\ In\ \Delta OBP, \angle OBP=90^0\\given\ that\ \angle APB=35^0\\ \angle AOB=360-90-90-35=145^0\\ in\ \Delta OAB,\ AO=BO=radius\\so\ \Delta OAB\ is\ an\ isosceles\ triangle\\thus\ \angle OAB=\angle OBA\\ \\in\ \Delta OAB;\\ \angle OAB+\angle OBA+\angle AOB=180\\\angle OAB+\angle OAB+145=180\\2 \angle OAB=180-145=35\\ \angle OAB= \frac{35}{2}\\\angle OAB=\boxed{17.5^0}


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