AB is tangent to O. If AO = 24 and BC = 27, what is AB?

Solution:

Given,

AB = ?, AO = 24, BC = 27

B0 = 51 ( 24 + 27)

Definition:

A line that touches the circle at a single point is known as a tangent to a circle.

The point where tangent meets the circle is called point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects.

By pythagoras theorem,

BO² = AB² + AO²

51² = X² + 24² .

2601 = X² + 576.

X² = 2601 - 576.

X² = 2025.

X = √2025

X = 45.

Therefore, AB = 45.

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AB is tangent to O. If AO = 24 and BC = 27, what is AB?

Summary:

AB is tangent to O. If AO = 24 and BC = 27, AB = 45.