Question

Find the value of x. If necessary, round your answer to the nearest tenth. O is the center of the circle. The figure is not drawn to scale.

Answer 1

x = 10

Explanation:

The radius of the circle is shown as x. That will be the measure of the hypotenuse of the right triangle with sides 6 and 8. You recognize these side lengths as having the ratio 3:4 (with a multiplier of 2), so you know that the hypotenuse will be 5 with a multiplier of 2. That is, x = 10.

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In case you're not familiar with a 3-4-5 right triangle, you can verify that the hypotenuse is 5 units using the Pythagorean theorem:

c = √(a^2 +b^2) = √(3^2 +4^2) = √25

c = 5

Multiplying the values by 2 gives ...

x = √(6^2 + 8^2) = √(36 +64) = √100

x = 10