Math Problem Statement
What is the radius of the small red circle
Solution
From the image, we have a square , where:
- units (since it is a square).
- There is a quarter circle with a radius equal to 4 units, and a smaller red circle with radius inside the square touching the quarter circle and the diagonal of the square.
Key Information:
- The quarter circle is centered at with radius 4.
- The diagonal of the square intersects the quarter circle and the smaller circle.
Approach:
-
Diagonal of the Square: The length of the diagonal of the square can be calculated using the Pythagorean theorem:
-
Distance from center of small circle to diagonal: Since the smaller red circle is tangent to both the quarter circle and the diagonal of the square, we can set up the geometry based on the tangency conditions. The relationship involves calculating the distance from the center of the red circle to the quarter circle and the diagonal.
Let me compute the radius of the small circle based on these tangency conditions.The radius of the small red circle is 2 units.
Would you like more details about how this was solved? Here are a few related questions you might consider:
- What is the length of the diagonal in a square in general?
- How does the tangency of circles work in geometry?
- Could the radius of the smaller circle change if the size of the square changes?
- What is the relationship between the quarter circle and the diagonal of the square?
- How does the Pythagorean theorem apply in finding diagonals?
Tip: When solving problems involving squares, diagonals are often a key component in connecting various geometric properties.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Pythagorean Theorem
Tangency
Formulas
Diagonal of square = √(side^2 + side^2)
Distance from the center of circle to tangents
Theorems
Pythagorean Theorem
Tangency condition of circles
Suitable Grade Level
Grades 9-11
Related Recommendation
Solving Geometric Problems Involving Tangent Circles
Finding the Diagonal Length of a Square with Inscribed Circles
Finding the Radius of the Largest Circle That Fits in a Square
Geometry Problem: Circles and Square with Tangents - Senior Kangaroo 2015
Find the Radius of the Larger Circle in a Square of Side 12 cm