Problem preview
G-C.4 Warmup M2-032-A06-V01

Construct a tangent line from an external point to a circle.

Solve an unknown using equal tangent segments

Problem

From external point \(P\), the \(\text{two}~\text{stated}~\text{segments}\) are tangent to the same circle: \(PA=18\) and \(PB=x\). Solve the unknown.

Big Picture

What this problem is really about

Equal tangent lengths are a whole-segment relationship, provided both segments start at the same external point and touch the same circle. We’ll verify those conditions, set the complete segment labels equal, and check that the solved value is a valid positive length.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.4
Category
Geometry
Domain
Circles
Objective
Construct a tangent line from an external point to a circle.
Problem type
Solve an unknown using equal tangent segments