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Tangent and Radius

Part of the Circles section of Coddy's Geometry journey. Lesson 48 of 62.

The tangent rule turns a tangent into a right angle. With the segment from the center to an outside point drawn, you get a right triangle: the radius, the tangent and the line to the center.

$Right triangle OTP with a 50 degree angle at O and 40 degrees at P$

Here TP is a tangent at T and the angle at O is 50°. No square is drawn at T, but the tangent rule gives 90° there. Then the triangle's angle sum gives the angle at P: 180° - 90° - 50° = 40°. On the board: tap the angle at T and pick Tangent and radius, then the angle at P and Angles in a triangle.

Challenge

TP is a tangent to circle O at T, and OT is a radius. Find ∠POT, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Circles

1Parts of a Circle

Center and Radius Chords and Diameters All Radii Are Equal Diameter Is Two Radii Recap: Parts of a Circle

4Arcs and Sectors

Arc Length Area of a Sector Find the Central Angle The Missing Central Angle Recap: Arcs and Sectors

7Angles in a Semicircle

Thales' Theorem The Right Angle Inside Is That Enough?Semicircle With Letters Recap: Semicircles

10Tangents

What a Tangent IsTangent and RadiusTangent Lengths Two Tangents From a Point Tangents With Letters Recap: Tangents