How do I find the area of the blue section in this trig circle problem?

In summary, the problem involves finding the area of a blue section in a sketch where the circles are all tangent and their radii are given. The suggested approach is to join the centers of the circles to form a triangle and calculate the area of the blue section as the difference between the area of the triangle and one-fourth of the area of each circle.
  • #1
onandon
3
0

Homework Statement


This is my own sketch of the problem. The radii are listed, and the circles are all tangent. I need to find the area of the blue part.

Homework Equations


The Attempt at a Solution


I've been staring at this for hours. I really have no idea where to start. I'm just looking for a push in the right direction.

Thanks for any help.

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
  • #2
Join centers of the circles to form a triangle with sides of 11,9 and 10 units. As you can see this triangle contains blue part+ quarter of each circle.
thus area of the blue part is:
area of the triangle joining centers - 1/4*(area of each circle)
 
  • #3
santapuri.1 said:
Join centers of the circles to form a triangle with sides of 11,9 and 10 units. As you can see this triangle contains blue part+ quarter of each circle.
thus area of the blue part is:
area of the triangle joining centers - 1/4*(area of each circle)

Thanks a ton!
 

FAQ: How do I find the area of the blue section in this trig circle problem?

What is a trig circle area problem?

A trig circle area problem is a type of mathematical problem that involves finding the area of a circle using trigonometric functions and formulas.

What are the basic steps for solving a trig circle area problem?

The basic steps for solving a trig circle area problem are:

  1. Determine the radius of the circle
  2. Use the formula A = πr2 to find the area of the circle
  3. Convert the angle measurements to radians if necessary
  4. Use trigonometric functions (such as sine, cosine, and tangent) to find the area of any sectors or segments within the circle
  5. Add the areas of the sectors or segments to the area of the whole circle to get the total area

What are some common applications of trig circle area problems?

Trig circle area problems are commonly used in various fields such as engineering, physics, and geometry. They can be used to calculate the area of circular objects or regions, such as a circular swimming pool, a circular piece of land, or the cross-sectional area of a pipe.

What are the most common trigonometric functions used in solving circle area problems?

The most commonly used trigonometric functions in solving circle area problems are sine, cosine, and tangent. These functions are used to find the lengths of sides or angles in a right triangle, which can then be used to calculate the area of sectors or segments within the circle.

What are some common mistakes to avoid when solving trig circle area problems?

Some common mistakes to avoid when solving trig circle area problems are:

  • Forgetting to convert angle measurements to radians if necessary
  • Using the wrong formula for finding the area of a sector or segment
  • Forgetting to add the areas of the sectors or segments to the area of the whole circle
  • Using the wrong units (such as using square inches instead of square feet) in the final answer

Similar threads

Find the Area of the Shaded Section in a Circle
Replies
12
Views
2K
Maximum area of a fenced-in half a circle
Replies
2
Views
2K
Area remaining of a quarter-circle deprived of these 3 inscribed circles
Replies
17
Views
3K
How do I find the circumference and Area of this figure?
Replies
24
Views
1K
Perimeter/Area of Shaded Region within a Circle
Replies
10
Views
23K
Finding Common Area of Two Circles
Replies
2
Views
2K
How Do Three Tangents Form an Equilateral Triangle Around a Circle?
Replies
7
Views
2K
Find the center of a circle given a tangent line & point
Replies
2
Views
3K
Can the Area of a Sector be Determined Without Calculus or Trig?
Replies
7
Views
2K
Circle and a line dividing the circumference
2
Replies
48
Views
4K

Hot Threads

Recent Insights

Back
Top