Problem preview

G-C.3 Warmup M2-031-A14-V03

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

Choose a triangle center from the required equal distances

Problem

\(\text{Three}~\text{towns}\) are represented by the vertices of a triangle, and a cell tower must be equally far from \(\text{all}~\text{three}\). Identify the appropriate triangle center, its defining construction lines, the equal-distance relationship, its circle role, and whether it must lie inside the triangle.

Answer choices

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Use the circumcenter without constructing its defining lines.

Use the circumcenter as a point equally distant from the three side lines.

Use the circumcenter: intersect side perpendicular bisectors to get a point equally distant from the three towns.

Use the incenter: intersect angle bisectors to get a point equally distant from the towns.

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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: Choose a triangle center from the required equal distances