Question

State and solve theorem 1st of circle of class 10th

Answer 1

Hey friend, Harish here.

Here is your answer. ( Refer to the image also )

Given that:

i) A circle with centre O.

ii) A tangent l touch the circle at the point A .

To Prove:

AO ⊥ Tangent L.

Construction:

Construct a Line OB where B is any point on the Tangent.

Proof:

We know that,

OC = OA

OB > OC

Then, OB > OA where "B" Is a random point taken on the tangent l.

When we construct some other line from O to any random point on the tangent, it is greater than OA.

So, OA being the shortest of all must be perpendicular to the tangent.

( Hence Proved )

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Hope my answer is helpful to you.