Question

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What is the value of n?

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n =
cm
Circle with two intersecting chords forming an x shape in the circle. The top left side of the x shape is labeled 4 centimeters. The top right side of the x shape is labeled 3 centimeters. The bottom left side of the x is labeled n. The bottom right side of the x is labeled 6 centimeters.

Answer 1

n = 8 cm

Explanation:

When two chords intersect each other inside a circle, the products of their segments are equal

Look to the attached figure

In the circle two chords are intersected at a point inside it

∵ The two chords are intersected in a point inside the circle

∴ The product of their segments are equal

∵ The segments of one chord are 4 centimeters and 6 centimeters

∵ The segments of the other chords are n and 3 centimeters

- Multiply each two segments and equate their products

∴ n × 3 = 4 × 6

∴ 3 n = 24

- Divide both sides by 3

∴ n = 8

∴ The value of n is 8 centimeters