10. POWER THEOREM.pptx mathematics quarter 2

math 10

1. POWER THEOREMS

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.

4. CHORD-CHORD THEOREM

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.

6. Secant-Secant Power Theorem

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.

8. Secant-Tangent Power Theorem

9. Solve for x. EXAMPLE 1:

10. 6(x) = 4(7) EXAMPLE 1: 6x = 28 6 6 x = 28/6 x = 4.67

11. Solve for x. EXAMPLE 2:

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

13. Solve for x. EXAMPLE 3:

14. x² = 9(9 + 16) EXAMPLE 3: x² = 9(15) x² = 225   x =  

15. QUICK CHECK: Solve for 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

17. QUICK CHECK: Solve for x.

18. QUICK CHECK: 8² = x(x + 12) 64 = x² + 12x 0 = x² + 12x - 64 0 = (x + 16) (x – 4) x = -16 x = 4

19. Seatwork (1 whole)

20. It’s Written Work Time!

21. Thank You for Listening!