Problem preview
G-C.2 Warmup M2-030-A08-V01

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

Use the tangent-radius relationship to identify a perpendicular angle

Problem

Consider this tangent configuration: radius \(OT\) meets tangent line \(PT\) at \(T\). What can you conclude from the tangent-radius relationship?

Big Picture

What this problem is really about

The tangent-radius theorem applies at the exact point where the radius meets the tangent line. We’ll identify the two rays meeting there, use perpendicularity, and name the right angle with the tangency point as its middle letter.

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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 the tangent-radius relationship to identify a perpendicular angle