10. POWER THEOREM.pptx mathematics quarter 2
- 2. Apply segment properties in a circle to solve problems. OBJECTIVE
- 3. CHORD-CHORD THEOREM If two chords intersect in a circle, then the products of the lengths of the chords segments are equal.
- 5. Secant-Secant Power Theorem If two secants intersect in the exterior of a circle, then the product of the measures of one secant segment and its external segment is equal to the product of the measures of the other secant and its external secant segment.
- 7. Secant-Tangent Power Theorem If a tangent and a secant intersect in the exterior of a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external secant segment.
- 10. 6(x) = 4(7) EXAMPLE 1: 6x = 28 6 6 x = 28/6 x = 4.67
- 12. 2(2+10) = x(x+5) EXAMPLE 2: 2(12) = x² + 5x 24 = x² + 5x 0 = x² + 5x - 24 0 = (x + 8)(x-3) x = -8 x = 3
- 14. x² = 9(9 + 16) EXAMPLE 3: x² = 9(15) x² = 225 √ x =
- 16. QUICK CHECK: 3(4) = x(7-x) 12 = 7x - x² x² - 7x + 12 = 0 (x – 4)(x – 3)= 0 x = 4 x = 3
- 18. QUICK CHECK: 8² = x(x + 12) 64 = x² + 12x 0 = x² + 12x - 64 0 = (x + 16) (x – 4) x = -16 x = 4
- 24. Thank You for Listening!
Editor's Notes
- #3: When two chords intersect inside a circle, each chord is divided into two segments. These segments are called chord segments.
- #5: A secant segment is a segment of a secant line that has exactly one endpoint on the circle. A secant segment that lies in the exterior of the circle is called an exterior secant segment. A special relationship exists between secants and external secant segments.
- #7: A tangent segment is both the exterior and whole segment because it is the segment of the tangent with one endpoint on the circle.