Question

PA and PB are tangent segment drawn from an external point P to a circle with centre O.if angleAOP=70°,find at what angle the two tangents are inclined to each other.​

Answer 1

PA and PB are tangent segment drawn from an external point P to a circle with centre O.if angleAOP=70°.

$In\: \triangle AOP , \angle {AOP} = 70\degree$

$\angle {OAP} = 90\degree \\\blue{ ( Tangent, radius \: relation )}$

$\underline {\pink { Angle \:sum \: property: }}$

$\angle {OAP} + \angle {AOP} + \angle {APO} = 180\degree$

$\implies 90\degree + 70\degree + \angle {APO} = 180\degree$

$\implies 160\degree + \angle {APO} = 180\degree$

$\implies \angle {APO} = 180\degree - 160\degree$

$\implies \angle {APO} = 20\degree$

$Now, \: \angle {APB} = 2\angle {APO} \\= 2\times 20 \\= 40\degree$

Therefore.,

$\red {\angle {APB} } \green { = 40\degree}$

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