Problem preview

G-C.2 Warmup M2-030-A11-V01

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

From the same external point, \(\text{two}~\text{tangent}~\text{segments}\) have lengths \(PA=12\) and \(PB=x\). Solve for the unknown.

Unworked circle diagram showing only the supplied geometric configuration and measures.

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What this problem is really about

Two tangent segments can be compared directly only when they start at the same external point and touch the same circle. We’ll verify that setup, set the segment lengths equal, and use the given labels to solve the unknown.

Answer choices

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x = 12

x = 6

x = 24

x = 0

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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