Geometrical properties of circle

In summary, the formula for calculating the circumference of a circle is C = 2πr, and the formula for calculating the area of a circle is A = πr^2. The diameter of a circle is twice the length of its radius, and both the circumference and area of a circle can be used to find its radius. The geometrical properties of a circle are used in various real-life applications, including engineering, architecture, and mathematics.
  • #1
LiHJ
43
2
DSC_0008.JPG

Homework Statement


Dear Mentors/PF helpers,

Please help me with part (ii), I couldn't find a way through this part.
DSC_0008.JPG


Homework Equations




The Attempt at a Solution


My solutions:
(i) angle RPS = 65 deg (angles in the same segment are equal)

(iii) angle PRS = 110 - 65 = 45 ( exterior angle of triangle PSR equal two interior angles)
angle PQS = angle PRS = 45 (angles in the same segment are equal)
 
Physics news on Phys.org
  • #2
Hint: Introduce the point C as center of the circle XPS to use the "touching" information.
 
  • #3
DSC_0011.JPG
 
  • #4
CSP should be PSC.

That is the same result I got.
 

FAQ: Geometrical properties of circle

1. What is the formula for calculating the circumference of a circle?

The formula for calculating the circumference of a circle is C = 2πr, where r is the radius of the circle and π is the mathematical constant pi (approximately equal to 3.14).

2. How do you find the area of a circle?

The formula for calculating the area of a circle is A = πr^2, where r is the radius of the circle and π is the mathematical constant pi (approximately equal to 3.14).

3. What is the relationship between the diameter and the radius of a circle?

The diameter of a circle is twice the length of its radius. This means that the diameter is equal to 2r, where r is the radius of the circle.

4. Can the circumference and area of a circle be used to find its radius?

Yes, the circumference and area of a circle can be used to find its radius. The formula for the circumference of a circle can be rearranged to solve for the radius (r = C/2π), while the formula for the area of a circle can be rearranged to solve for the radius (r = √(A/π)).

5. How are the geometrical properties of a circle used in real life?

The geometrical properties of a circle are used in many real-life applications, such as in engineering, architecture, and design. For example, the shape of a circle is often used in the design of wheels and gears, and the properties of circles are used in constructing circular buildings and structures. The concept of a circle is also important in mathematics and science, as it serves as a foundation for more complex geometrical concepts and equations.

Similar threads

Replies
6
Views
2K
Replies
1
Views
1K
Replies
2
Views
1K
Replies
1
Views
969
Replies
3
Views
2K
Replies
5
Views
2K
Replies
5
Views
10K
Back
Top