Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 34: Chapter 34

Problem 618

Next question

Using a straight edge only, construct the perpendicular to a given diameter of a circle from any point off the diameter.

Short Answer

Expert verified
To construct the perpendicular to a given diameter of a circle from any point off the diameter using a straight edge only, follow these steps: 1. Draw the circle and its diameter, labeling endpoints as A and B. 2. Choose a point outside the diameter, label it as C. 3. Connect C to A and C to B using straight edge. 4. Construct midpoints M and N of segments CA and CB, respectively. 5. Draw a line through points M and N, extending beyond the circle. 6. Find the intersection point D of this line with the circle. 7. Connect point C to D, which is the perpendicular to diameter AB.
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Draw the circle and diameter

First, draw a circle and the diameter of the circle. Label the diameter as AB, where A and B are the endpoints of the diameter.

Step 2: Select a point outside the diameter

Choose a point outside the diameter of the circle; label this point as C.

Step 3: Connect C to A and B

Using the straight edge, draw a line segment connecting point C to point A and another line segment connecting point C to point B.

Step 4: Construct midpoints

Construct the midpoint of line segment CA and the midpoint of line segment CB. Label the midpoints as M and N, respectively.

Step 5: Draw lines through the midpoints

Using the straight edge, draw a line through points M and N, extending beyond the circle.

Step 6: Find the intersection point

Identify the intersection point of the line through points M and N with the original circle. Label this point as D.

Step 7: Draw the perpendicular to the diameter

Using the straight edge, draw the line segment connecting point C to point D. This line segment CD is the required perpendicular to the diameter AB. In conclusion, by following these steps and using a straight edge only, we were able to construct the perpendicular to a given diameter of a circle from a point outside the diameter.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 34

Given two circles at fixed locations, find the line that cuts equal chords in both of them.
Chapter 34

Construct a regular decagon.
Chapter 34

Construct the product of 2 and \(4(1 / 2)\).
Chapter 34

Inscribe a square in a given semicircle.
Chapter 34

Given the unit length below, construct a segment of length \(\sqrt{3}\)
See all solutions

More chapters from the book ‘Geometry’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Pure Maths

Read Explanation
Math

Calculus

Read Explanation
Math

Decision Maths

Read Explanation
Math

Statistics

Read Explanation
Math

Geometry

Read Explanation
Math

Mechanics Maths

Read Explanation
View all explanations