Problem preview

G-C.3 Core M2-031-R02-V03

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

Find and verify a coordinate circumcenter

Problem

For \(G(1,~1)\), \(H(5,~1)\), and \(J(3,~5)\), use symmetry and perpendicular-bisector relationships to find the circumcenter. Verify the \(\text{three}~\text{equal}~\text{squared}~\text{distances}\), then state the radius and center-radius equation of the circle.

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O = (3, 5/2), OG = OH = OJ = 5/2, and (x − 3)² + (y − 5/2)² = 25/4.

O = (3, 5/2), OG = OH = OJ = 5/2, and (x − 3)² + (y − 5/2)² = 5/2.

O = (3, 1), OG = OH = OJ = 2, and (x − 3)² + (y − 1)² = 4.

O = (3, 7/3), OG = OH = OJ = 5/2, and (x − 3)² + (y − 7/3)² = 25/4.

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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: Find and verify a coordinate circumcenter