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G-GPE.4 Warmup M2-043-A07-V01

Use coordinates to prove simple geometric theorems, including simple circle theorems.

Verify or reject a coordinate tangent claim

Problem

Verify the tangent claim from complete coordinate evidence: circle centered \(O=(0,0)\) through \(T=(5,0)\); candidate line \(x=5\) through \(T\).

Neutral coordinate reference: center O (0, 0), circle through T (5, 0), and candidate line x equals 5 through T; no circle, radius, line, or tangent conclusion is drawn. Open full size
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What this problem is really about

A tangent claim needs both contact and direction evidence. We’ll verify that the proposed point lies on the circle and candidate line, determine the radius direction from center to contact point, compare it with the line’s direction, and invoke the radius-tangent theorem only after incidence and perpendicularity both hold.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-GPE.4
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Use coordinates to prove simple geometric theorems, including simple circle theorems.
Problem type
Verify or reject a coordinate tangent claim