1. W ARM - UP : S OLVE IN YOUR NOTEBOOK 1. 8x = 12 2. 8(10+8)=6(y+6) 3. 10 2 =6(2x+8) 4. 12 2 =x(x+6)

2. W ARM U P Find the missing values in the diagrams below. 1. 2. y=90, x=46, z=44

3. A, B, AND C ARE THREE EXTERIOR POINTS OF THE CIRCLE WITH CENTRE O. T HE TANGENTS AP, BQ, AND CR ARE OF LENGTHS 3 CM, 4 CM, AND 3.5 CM RESPECTIVELY. F IND THE PERIMETER OF TRIANGLE ABC. Perimeter of triangle ABC = (7 + 7.5 + 6.5) cm = 21 cm

4. C HAPTER 10.5 Segment Lengths in Circles

5. T HEOREM 10.15 If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

6. F IND THE VALUE OF X 1. 2. 3. 915 20 8.5 2

7. T HEOREM 10.16 If two secant segments share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment.

8. F IND VALUE OF X 1. 2. 3.

9. T HEOREM 10.17 If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the length of the secant segment and the length of its external segment equals the square of the length of the tangent segment.

10. F IND THE VALUE OF X 1. 2. 24 8

11. You are standing at point C, about 8 feet from a circular aquarium tank. The distance from you to a point of tangency on the tank is about 20 feet. Estimate the radius of the tank.

12. A C HALLENGE ! Find x and y 1. 2. 3. x=42, y=10