Problem 36 of 7
Explain why the constructed line YZ is tangent to the circle centered at P.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
use right angle in semicircle and radius-tangent perpendicularity.
Hidden until you reveal it.
Explanation must use right angle in semicircle and radius-tangent perpendicularity.
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Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Use the auxiliary circle diameter to establish a right angle at the tangent point.
2. Identify the radius to that point.
3. Apply the theorem that a line perpendicular to a radius at the circle is tangent.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Simply saying the line touches the circle without proof.