WARM-UP: SOLVE IN YOUR NOTEBOOK

1. 8x = 122. 8(10+8)=6(y

+6)3. 102=6(2x+8)4. 122=x(x+6)

€

x =1.5y =18

x = 413

x = −3 ± 3 17

WARM UPFind the missing values in the diagrams below.

1. 2.

y=90, x=46, z=44

€

4 3

A, B, AND C ARE THREE EXTERIOR POINTS OF THE CIRCLE WITH CENTRE O. THE TANGENTS AP, BQ, AND CR ARE OF LENGTHS 3 CM, 4 CM, AND 3.5 CM RESPECTIVELY. FIND THE PERIMETER OF TRIANGLE ABC.

Perimeter of triangle ABC = (7 + 7.5 + 6.5) cm = 21 cm

CHAPTER 10.5Segment Lengths in Circles

THEOREM 10.15If 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.

FIND THE VALUE OF X

1.2. 3.

9 15

20

8.5 2

THEOREM 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.

FIND VALUE OF X1. 2.

3.

€

4313

€

−29 + 38412

≈16.49

€

823

THEOREM 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.

FIND THE VALUE OF X1. 2.

24 8

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.

A CHALLENGE! Find x and y

1.2.

3.

x=42, y=10€

x =12, y = 2 13 ≈ 7.21

€

x = 7, y =-13 +5 17

2≈ 3.81