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G-C.2 Warmup M2-030-A10-V01

Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.

Use a perpendicular from the center to a chord to find the chord length

Problem

A radius of length \(13\) is perpendicular from the center to chord \(AB\), and the center-to-chord distance is \(5\). Find the chord length.

Unworked circle diagram showing only the supplied geometric configuration and measures. Open full size
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What this problem is really about

The key geometric move happens before the Pythagorean theorem: a perpendicular from the center bisects the chord, so the unknown leg represents only half the chord. We’ll build the right triangle with the radius as hypotenuse, solve for the nonnegative half-length, and then return to the full chord.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.2
Category
Geometry
Domain
Circles
Objective
Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.
Problem type
Use a perpendicular from the center to a chord to find the chord length