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G-C.2 Warmup M2-030-A11-V04

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

Solve for an unknown using equal tangent segments from the same external point

Problem

Point \(T\) is outside a circle. Tangent segments \(TA\) and \(TB\) are drawn to the circle, with lengths \(TA=4x-1\) and \(TB=19\). Solve for \(x\).

Unworked circle diagram showing only the supplied geometric configuration and measures. Open full size
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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
Solve for an unknown using equal tangent segments from the same external point