Question

what is the relation between the tangent drawn to a circle at the ends of its longest chord​

Answer 1

Answer:

length of the tangents will be equal.

Answer 2

Given:

Here is a circle and tangent is drawn at the ends of its longest chord.

To Find:

What is the relation between the tangent drawn to a circle at the ends of its longest chord​?

Solution:

We know that diameter is the longest chord of circle. Here a circle is drawn with centre O. A diameter is drawn pass through centre of circle.

Point A and point B are end point of diameter. A tangent LM and XY is drawn from point A and point B. It is clear from figure:

∠LAB = 90°     (∵ Tangent is perpendicular to diameter)

∠YBA = 90°     (∵ Tangent is perpendicular to diameter)

From figure it is clear that AB is transversal line to XY and LM:

Then ∠LAB and ∠YBA will be alternate interior angle:

∠YBA = ∠LAB =90°     ( Alternate interior angle)

So line XY and LM will be parallel to each other because their alternate angle are equal.

There will be parallel relation between the tangent drawn to a circle at the ends of its longest chord.