Ptolemy's Theorem Quiz
10 Questions
2 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is Ptolemy's theorem about?

  • The relation between the sides and diagonals of a cyclic quadrilateral (correct)
  • The calculation of angles in a triangle
  • The properties of a regular polygon
  • The measurement of circles and arcs

    • How is Ptolemy's theorem verbally expressed?

  • AB + CD = AC - BD + BC ⋅ AD
  • AB ⋅ CD = AC + BD - BC ⋅ AD
  • AC ⋅ BD = AB ⋅ CD + BC ⋅ AD (correct)
  • AB ⋅ CD + BC ⋅ AD = AC ⋅ BD

    • What does the converse of Ptolemy's theorem state?

  • If the sum of the products of the lengths of its two pairs of opposite sides is equal to the product of the lengths of its diagonals, then the quadrilateral can be inscribed in a circle (correct)
  • If the quadrilateral is a rectangle, then the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the pairs of opposite sides
  • If the quadrilateral is not cyclic, then the product of the lengths of its diagonals is equal to the sum of the products of the lengths of the pairs of opposite sides
  • If the sum of the lengths of the sides is equal to the product of the lengths of the diagonals, then the quadrilateral is cyclic

    • What does Ptolemy's theorem yield as a corollary regarding an equilateral triangle inscribed in a circle?

    <p>A pretty theorem regarding an equilateral triangle inscribed in a circle and a point on the circle</p> Signup and view all the answers

    What does the corollary regarding an equilateral triangle inscribed in a circle state?

    <p>The product of the distances from a point to the vertices of the equilateral triangle is equal to the radius of the circle</p> Signup and view all the answers

    What do NCERT Solutions for Class 8 Maths Chapter 8 aim to provide?

    <p>Skill-building exercises tailored to students' strengths and interests</p> Signup and view all the answers

    How do the NCERT Solutions for Class 8 Maths Chapter 8 help students in exam preparation?

    <p>Boost confidence for taking up CBSE Class 8 Maths exams</p> Signup and view all the answers

    What advantage do students gain by solving the exercise questions in the NCERT textbook?

    <p>Preparing themselves well ahead of the final CBSE exams</p> Signup and view all the answers

    What kind of aid are the Grade 8 NCERT Solutions for Class 8 Maths to students?

    <p>An invaluable aid for exam preparations</p> Signup and view all the answers

    What is the primary focus of NCERT Solutions for Class 8 Maths Chapter 8?

    <p>To the point and not confusing, helping students in reaching a conclusion using the ideal problem-solving method</p> Signup and view all the answers

    Study Notes

    Ptolemy's Theorem

    • Ptolemy's theorem is a mathematical concept that relates to the geometry of a cyclic quadrilateral.
    • Verbal expression of Ptolemy's theorem: "The sum of the products of the opposite sides of a cyclic quadrilateral is equal to the product of the diagonals."
    • The converse of Ptolemy's theorem states that if the sum of the products of the opposite sides of a quadrilateral is equal to the product of the diagonals, then the quadrilateral is cyclic.

    Corollary Regarding Equilateral Triangle

    • Ptolemy's theorem yields a corollary regarding an equilateral triangle inscribed in a circle, stating that the product of the sides of the equilateral triangle is equal to three times the square of the radius of the circle.
    • The corollary states that if an equilateral triangle is inscribed in a circle, then the product of the sides of the triangle is equal to three times the square of the radius of the circle.

    NCERT Solutions for Class 8 Maths Chapter 8

    • NCERT Solutions for Class 8 Maths Chapter 8 aim to provide comprehensive and step-by-step solutions to the exercise questions in the NCERT textbook.
    • The solutions help students in exam preparation by providing clear and concise explanations of the concepts and formulas.
    • By solving the exercise questions in the NCERT textbook, students gain a thorough understanding of the concepts and are able to apply them to solve problems.
    • The Grade 8 NCERT Solutions for Class 8 Maths serve as a valuable aid to students, providing them with a reliable and trustworthy resource to prepare for their exams.
    • The primary focus of NCERT Solutions for Class 8 Maths Chapter 8 is to provide students with a solid understanding of the mathematical concepts and to help them develop their problem-solving skills.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Test your knowledge of Ptolemy's theorem and its application in Euclidean geometry with this quiz. Explore the relationship between the sides and diagonals of cyclic quadrilaterals and discover the historical significance of the theorem in the work of the Greek astronomer and mathematician, Ptolemy.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser