The document discusses central angles and circumference angles in circles. A central angle is an angle inside a circle whose vertex is the center of the circle. A circumference angle is an angle whose vertex is located on the circumference of the circle. The central angle is twice the size of the circumference angle that subtends the same arc. Circumference angles that are subtended by the same arc are equal. Angles subtended by the diameter of a circle, forming a semicircle, are right angles. The document also discusses cyclic quadrilaterals, which have all four vertices lying on the circumference of a single circle, meaning the opposite angles of a cyclic quadrilateral are supplementary.

1. ANGLES IN A CIRCLE : Central Angle and Circumference Angle Math Is the Best Grade 8 Semester 2 Cyclic Quadrilateral

2. Angles in Circle Central & Circumference Angle Central Angle is an angle inside a circle whose vertex is the center of the circle Circumference Angle is an angle whose vertex located on the circumference of the circle is central angle is circumference angle O A B P R Q

3. Angles in Circle Central & Circumference Angle In the diagram at right, chords AC and BC form the angle ACB. We say that arc AB has subtended angle ACB. The central angle is twice the circumferenc e angle, standing on the same arc. Or b = 2a All circumference angles are subtended by the same arc are equal. a = b = c Angles subtended by the diameter, that is, angles in a semicircle, are right angles Or The circumference angles subtended by the diameter are right angles

4. Angles in Circle Central & Circumference Angle Examples Find the values of the pronumerals in each of the following

5. Angles in Circle Cyclic Quadrilaterals CYCLIC QUADRILATERALS A cyclic quadrilateral has all four vertices on the circumference of a circle; that is, the quadrilateral is inscribed in the circle. In the diagram at right points A, B, C and D lie on the circumference and, hence, ABCD is a cyclic quadrilateral. It can also be said that points A, B, C and D are concyclic; that is, the circle passes through all the points.

6. Angles in Circle Cyclic Quadrilaterals The opposite angles of a cyclic quadrilateral are supplementary (add to 180°). The converse is also true: If opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic.

7. Angles in Circle Cyclic Quadrilaterals

8. Angles in Circle Cyclic Quadrilaterals Exercises

9. Angles in Circle Cyclic Quadrilaterals

10. Creating Math for better living Thank you Angles in Circle Cyclic Quadrilaterals