Question

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.​

Answer 1

Step-by-step explanation:

टुडे जनागल बॉम्बे सप्लीमेंट्री क्वेश्चन फ्रॉम क्लास 10th यू कैन चेक आउट

Answer 2

Answer:

a external point P. PA and PB are the tangents.

As radius of the circle is perpendicular to the tangent.

OA⊥PA

Similarly OB⊥PB

∠OBP=90

o

∠OAP=90

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In Quadrilateral OAPB, sum of all interior angles =360

o

⇒∠OAP+∠OBP+∠BOA+∠APB=360

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⇒90

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+90

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+∠BOA+∠APB=360

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∠BOA+∠APB=180

o

It proves the angle between the two tangents drawn from an external point to a circle supplementary to the angle subtented by the line segment

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