Question

Prove that, If a line is in the plane of a circle such that it is perpendicular to the radius ofthe circle at its end. Point on the circle, then the line is tangent to the circle.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given:

line perpendicular to the radius of the circle.

To Prove:

The line if the tangent of the circle.

Proof:

1) As we all know that the circle have the equal tangent if they are drawn from any point outside the circle.

2) so we will apply the rule of similarity to prove the above condition.

• In ΔABO & ΔAOC

     OC = OB ( radius of the same circle)

     ∠C = ∠B = 90°  (line is perpendicular to the radius the the circle)

    AO = AO (common)

ΔAOB ≅ ΔAOC ( by RHS)

AC = BC ( by CPCT)

• As it is very clear that the tangent are equal to each other so the given line are the tangent of the circle.