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The Joy of a Teacher is the Success of his Students. - Samuel Chukwuemeka

Theorems on Circles

Samuel Dominic Chukwuemeka (SamDom For Peace)

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.

Circle Theorem 1

(2.) Angles in the same segment of a circle are equal.

Circle Theorem 2

(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.

Circle Theorem 3

(4.) The sum of the interior opposite angles of a cyclic quadrilateral is $180^\circ$

Circle Theorem 4

(5.) The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

Circle Theorem 5

(6.) The radius of a circle is perpendicular to the tangent of the circle at the point of contact.

Circle Theorem 6

(7.) Two tangents drawn from the same external point are equal in length.

Circle Theorem 7

(8.) The angle between a tangent and a chord is equal to the angle in the alternate segment.

Circle Theorem 8


Chukwuemeka, S.D (2016, April 30). Samuel Chukwuemeka Tutorials - Math, Science, and Technology. Retrieved from

CrackACT. (n.d.). Retrieved from

CAREER INDIA. (n.d). Retrieved from

CSEC Math Tutor. (n.d). Retrieved from

MySchoolGist - Free West African Senior School Certificate Examination (WASSCE) Past Questions. (n.d). Retrieved from

VAST LEARNERS. (n.d). Retrieved from