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Angles in a Circle: Central, Circumference, and Cyclic Quadrilaterals
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.
