Enough to Find It?

Part of the Circles section of Coddy's Geometry journey. Lesson 55 of 62.

Before a long chase, ask whether the figure fixes the angle at all. Count what you know: each marked angle, each right angle a diameter or a tangent gives, each pair of radii. If a road of rules reaches the angle, the answer is Yes. If the angle can still change while every marked fact stays true, it is No.

$Diameter AB with P and Q on the circle and no angles marked$

Here no angle is marked. The diameter fixes the angle at P at 90°, but slide P round the circle and every other angle moves. So nothing else is fixed. Mark one angle at A and the right triangle APB is settled, and the circle rules can carry that onward.

If you answer Yes, the board asks you to finish the chase.

Challenge

AB is a diameter of circle O, and P and Q are on the circle. Is there enough information to find ∠AQP? Answer, and if it is Yes, finish the chase. Then press Check.

Try it yourself

$Is there enough information?$

Is there enough information?

Test yourself

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

All lessons in Circles

2Circumference

Around the Circle Using the Diameter Radius From Circumference Circumference With Letters Recap: Circumference

5Radii Make Isosceles

Two Radii, One Triangle Base Angles From the Center The Angle at the Center Isosceles With Letters Recap: Radii and Triangles

8Angles on the Same Arc

Same Arc, Same Angle Using the Same Arc Spot the Bow Tie Same Arc With Letters Recap: Same Arc

11Circle Chases

Tangent Meets Chord Two Roads to One AngleEnough to Find It?Cyclic Meets Isosceles Recap: Circle Chases