For Exercises 8-12, first make a sketch of what you are...

For Exercises $8-12,$ first make a sketch of what you are trying to construct and label it. Then use the segments below, with lengths $r, s,$ and $t$. (UNDERLINE CANT COPY). Construct two congruent, externally tangent circles with radius $s$. Then construct a third circle that is both congruent and externally tangent to the two circles.

For Exercises $8-12,$ first make a sketch of what you are trying to construct and label it. Then use the segments below, with lengths $r, s,$ and $t$.
(UNDERLINE CANT COPY).
Construct two congruent, externally tangent circles with radius $s$. Then construct a third circle that is both congruent and externally tangent to the two circles.

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Key Concepts

Use of Given Segments

Utilizing segments of specified lengths is essential in geometric constructions to maintain proportional relationships. These segments act as measurement standards, allowing for the replication of distances and ensuring that constructed figures meet the given conditions.

Tangency

Tangency refers to the condition where two figures touch at exactly one point without intersecting. External tangency, in particular, involves circles that meet at a single point on their outer boundaries, meaning their interiors do not overlap.

Geometric Constructions

This concept involves creating geometric figures using only a compass and straightedge, following the rules of Euclidean geometry. It emphasizes precision and the use of basic tools to replicate lengths, angles, and other geometric relationships accurately.

Circle Congruence

Circle congruence means that the circles are identical in size, having equal radii. When constructing congruent circles, one ensures that each circle’s radius is the same, which is fundamental for establishing equal geometric properties among them.

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