Geometry Puzzle – Challenge 77
This is a great math puzzle and critical thinking challenge that is sure to get you thinking!
Challenge:
What is the perimeter of the inscribed equilateral triangle, if the diameter of the circle above is 4?
A- \(4\sqrt{2}\)
B- \(4\sqrt{3}\)
C- \(6\sqrt{2}\)
D- \(6\sqrt{3}\)
E- 12
The Absolute Best Book to Challenge Your Smart Student!
Original price was: $16.99.$11.99Current price is: $11.99.
Satisfied 123 Students
The correct answer is D.
Draw the bisector of the angle A perpendicular to line BC.
D is the center of the circle and CD is equal to the radius. The diameter of the circle above is 4. So, CD is 2.
Triangle CDE is a 30-60-90 degree triangle and angle DCE is 30.
Since, CD is 2 (the hypotenuse of the triangle CDE), DE is 1 and CE is \(\sqrt{3}\). Why?
Therefore, BC is \(2\sqrt{3} \) and the perimeter of the triangle ABC is
\(3 × 2\sqrt{3} = 6\sqrt{3}\)
The Best Books to Ace Algebra
Original price was: $29.99.$14.99Current price is: $14.99.
Original price was: $29.99.$14.99Current price is: $14.99.
Satisfied 1 Students
Original price was: $24.99.$14.99Current price is: $14.99.
Satisfied 92 Students
Original price was: $24.99.$15.99Current price is: $15.99.
Satisfied 125 Students
Related to This Article
More math articles
- 10 Most Common 6th Grade PARCC Math Questions
- 7th Grade KAP Math Worksheets: FREE & Printable
- Algebra Puzzle – Challenge 43
- The Ultimate Ready to Work Algebra 1 Course (+FREE Worksheets)
- What Kind of Math Is on the ASVAB Test?
- How to Use Area Models to Multiply One-Digit Numbers By Up to 4-digit Numbers
- Let’s Chat: How to Simplify the Steps to Solve Two-step Equations
- 6th Grade PSSA Math FREE Sample Practice Questions
- How to Write the Equation of a Cosine Graph?
- FREE 3rd Grade NYSE Math Practice Test
What people say about "Geometry Puzzle – Challenge 77 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.