Final: Paths to the Pond

Part of the Circles section of Coddy's Geometry journey. Lesson 56 of 59.

A round pond has its center at O and a radius of 8 meters. From a bench at P, 17 meters from the center, two straight paths run to the edge of the pond and just touch it, at T and at U. How long is the path from P to U?

Challenge

PT and PU are the two paths, tangents to the pond from P. The radius OT and the distance OP are marked. Find PU, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

All lessons in Circles

1Parts of a Circle

Center and Radius Chords and Diameters 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 Is Tangent and Radius Tangent Lengths Two Tangents From a Point Tangents With Letters Recap: Tangents

2Circumference

The Hexagon Inside Around the Circle Radius From Circumference 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 Angle Enough to Find It?Cyclic Meets Isosceles Recap: Circle Chases

3Area of a Circle

The Area Formula Area From the Diameter Radius From the Area Circumference to Area Recap: Area of a Circle

6Inscribed Angles

Meet the Inscribed Angle Half the Central Angle Twice the Inscribed Angle The Big Arc Inscribed With Letters Recap: Inscribed Angles

9Cyclic Quadrilaterals

Four Corners on a Circle Opposite Angles Add to 180 Is It Cyclic?Cyclic With Letters Recap: Cyclic Quadrilaterals

12Final Challenges

Final: The Pizza SliceFinal: Paths to the PondFinal: The Curved Track Final: Deep in the Circle Final: Angle Into Arc