Semicircle With Letters

Part of the Circles section of Coddy's Geometry journey. Lesson 35 of 62.

When the angle at the circle carries a letter, the semicircle rule gives the simplest equation in this section: the label equals 90.

$Angle 3x at P standing on the diameter AB$

Here the angle at P is 3x° and it stands on the diameter AB. The rule says 3x = 90, so x = 30. The point is not the algebra: it is seeing the diameter and knowing the angle is 90° without being told.

Challenge

AB is a diameter of circle O and P is on the circle. Tap the angle at P, pick the rule that gives it, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

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 LettersRecap: Semicircles

10Tangents

What a Tangent Is Tangent and Radius Tangent Lengths Two Tangents From a Point Tangents With Letters Recap: Tangents