Question

In the diagram, the radius is 7 and tangent AB has length of 24. Determine the length of OA rounded to the nearest whole number

Answer 1

Given the radius r and the tangent line AB, the length of the line OA is 24 units

How to determine the length OA?

The radius r and the tangent line AB meet at a right angle.

By Pythagoras theorem, we have:

AB² = OA² + r²

So, we have:

24² = OA² + 7²

Rewrite as:

OA² = 24² - 7²

Evaluate

OA² = 527

Take the square root of both sides

OA = 23

Hence, the length of OA is 24 units

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