For in GOD we live, and move, and have our being.
- Acts 17:28
The Joy of a Teacher is the Success of his Students.
- Samuel Chukwuemeka
Theorems on Circles
I greet you this day,
First: read the notes.
Second: view the videos.
Third: solve the questions/solved examples.
Fourth: check your solutions with my thoroughly-explained examples.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting!!!
Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S
Symbols and Meanings
- $r$ = radius
- $d$ = diameter
- $\pi = pi = \dfrac{22}{7}$
- $A$ = area
- $C$ = circumference
Formulas
- To solve for a specified variable for each formula, please review Solved Examples - Literal Equations
- $d = 2r$
- $r = \dfrac{d}{2}$
- $C = \pi d$
- $C = 2\pi r$
- $A = \pi r^2$
- $A = \dfrac{\pi d^2}{4}$
Circle Theorems
(1.) The angle in a semicircle is a right angle.
(2.) Angles in the same segment of a circle are equal.
(3.) The angle which an arc of a circle subtends at the center is twice the angle which the same arc of the circle subtends at the circumference.
(4.) The sum of the interior opposite angles of a cyclic quadrilateral is $180^\circ$
(5.) The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
(6.) The radius of a circle is perpendicular to the tangent of the circle at the point of contact.
(7.) Two tangents drawn from the same external point are equal in length.
(8.) The angle between a tangent and a chord is equal to the angle in the alternate segment.
References
Chukwuemeka, S.D (2016, April 30). Samuel Chukwuemeka Tutorials - Math, Science, and Technology.
Retrieved from https://www.samuelchukwuemeka.com
CrackACT. (n.d.). Retrieved from http://www.crackact.com/act-downloads/
CMAT Question Papers CMAT Previous Year Question Bank - Careerindia. (n.d.). Https://Www.Careerindia.Com. Retrieved May 30, 2020, from https://www.careerindia.com/entrance-exam/cmat-question-papers-e23.html
CSEC Math Tutor. (n.d). Retrieved from https://www.csecmathtutor.com/past-papers.html
Free Jamb Past Questions And Answer For All Subject 2020. (2020, January 31). Vastlearners. https://www.vastlearners.com/free-jamb-past-questions/
Mathematics. (n.d.). Waeconline.Org.Ng. Retrieved May 30, 2020, from https://waeconline.org.ng/e-learning/Mathematics/mathsmain.html
NSC Examinations. (n.d.). www.education.gov.za. https://www.education.gov.za/Curriculum/NationalSeniorCertificate(NSC)Examinations.aspx