Problem preview

G-C.3 Core M2-031-R05-V04

Construct inscribed/circumscribed circles of triangles and prove angle properties of cyclic quadrilaterals.

Use an incenter's perpendicular radius

Problem

A coordinate triangle has incenter \(I~=~(2,~3)\) and side \(BC\) on \(x~=~5\). Find the perpendicular foot \(U\), use \(IU\) as the incircle radius, justify the tangency at \(U\), and write the incircle equation.

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The circle is centered at U = (5, 3) with radius 3: (x − 5)² + (y − 3)² = 9.

U = (5, 3), radius 3/2, and (x − 2)² + (y − 3)² = 9/4 because IU is the diameter.

U = (5, 3), radius 3, and (x − 2)² + (y − 3)² = 9 because IU is parallel to x = 5.

U = (5, 3), radius IU = 3, and the incircle is (x − 2)² + (y − 3)² = 9 because IU is perpendicular to x = 5.

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Curriculum context

Course: Math II
Standard: G-C.3
Category: Geometry
Domain: Circles
Objective: Construct inscribed/circumscribed circles of triangles and prove angle properties of cyclic quadrilaterals.
Problem type: Use an incenter's perpendicular radius