Question

Prove that tangent at any point is perpendicular to radius through point of contact.

Answer 1

Step-by-step explanation:

Proof: OP is perpendicular to AB.

Construction:

Let a point Q on XY, other than P. O and Q is joined.

The point Q lies outside the circle because AB is a tangent.{Every point on the tangent to a circle lies outside the circle}

Let OQ intersect the circle in R.

OQ = OR + RQ

⇒ OQ > OR

⇒ OQ > OP

Thus, OQ is longer than OP.

OP < OQ

Thus, OP is the shortest of all the distances of the point O to the tangent AB.

∴ OP ⊥ AB.

≅ Hence proved!

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Answer 2

Step-by-step explanation:

see the attached image above......

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