Problem preview

G-C.3 Warmup M2-031-A14-V02

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

Choose a triangle center from the required equal distances

Problem

A fountain must be equally far from \(\text{all}~\text{three}~\text{side}~\text{lines}\) of a triangular plaza. Identify the appropriate triangle center, its defining construction lines, the equal-distance relationship, its circle role, and whether it is guaranteed to lie inside the plaza.

Source triangular plaza with the three side lines identified as the equal-distance targets.

Answer choices

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Preview only

Use the incenter without constructing its defining lines.

Use the incenter as a point equally distant from the three vertices.

Use the circumcenter to get equal distances to the side lines.

Use the incenter: intersect the interior angle bisectors. Their intersection has equal perpendicular distances to all three sides, is the center of the circle tangent to all three sides, and is always inside the triangle.

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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