Exercises: Constructing Tangent Lines From an External Point

Grade 10·21 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-c-a-4

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Fluency Practice

In the tangent construction, the auxiliary circle has $OP$ as its diameter. Why must its center be at the midpoint $M$ of $OP$ ?

Because $M$ is equidistant from $T_1$ and $T_2$ .

Because a circle with diameter $OP$ has its center at the midpoint of $OP$ , which is $M$ .

Because the center must be on the original circle.

Because $M$ is the midpoint of $T_1T_2$ .