Which Tangents Are Actually Equal?

Understand the problem

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First, understand the question

Do not start calculating until the given information and the required answer are clear.

Problem

A circle touches sides ABAB and ACAC at PP and QQ. Decide which tangent segments must be equal.

What are we trying to do?

Identify equal tangent segments by checking that both start from the same external point.

Use the visual to test the rule

Use the control to change the mathematical situation and watch what remains true.

ABCPQR

Choose one starting vertex

Tap a vertex. Watch where its two tangent segments end.

Helpful?