Tangents Secants and Circles...Oh My

Geometry Level 1

In the above diagram, line segment $\overline{PT}$ is tangent to both circle $O$ and circle $O'.$ Given the following three lengths: $\lvert\overline{AB}\rvert = 35, \lvert\overline{PC}\rvert = 30, \lvert\overline{CD}\rvert = 20,$ what is $\lvert\overline{PA}\rvert?$

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Tangents Secants and Circles...Oh My

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.