1. TODAY IN GEOMETRY…
Stats on Ch. 8 Test
Learning Target : 10.1 Use properties of tangents of a circle
Independent practice

2. NUMBER OF STUDENTS WHO TOOK THE CH.8 TEST (33 pts.)
HOW DID YOU “SHAPE” UP??
Results for ALL of my Geometry classes:
GRADE
NUMBER OF STUDENTS WHO TOOK THE CH.8 TEST (33 pts.)
1ST PERIOD
2ND PERIOD
4TH PERIOD
6TH PERIOD
TOTAL A 10 2 12 34 B 11 5 9 7 32 C 6 16 D 1 4 8 F
Avg.
26.13
27.88
25.71
28.80
27.13

3. CIRCLE: Set of all points in a plane that are equidistant from a given point called the center.
Middle of the circle.
CENTER

4. RADIUS: Distance from the center of a circle to the edge of the circle.𝑟 𝑟 𝑟

5. CHORD: Segment whose endpoints are on a circle.

6. DIAMETER: A chord that contains the center of the circle.
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓=𝟐∙𝒓𝒂𝒅𝒊𝒖𝒔 𝑟 𝑑

7. PRACTICE: Use the diagram to find the given lengths.
e. Radius of circle C
f. Diameter of circle C
g. Radius of circle D
h. Diameter of circle D
SOLUTION
3 units
6 units
2 units
4 units
3 units
6 units
2 units
4 units

8. SECANT: A line that intersects a circle in two points.

9. TANGENT: A line that intersects a circle in exactly ONE point
TANGENT: A line that intersects a circle in exactly ONE point. (JUST TOUCHES the circle)
Point of tangency

10. PRACTICE:
SOLUTION:
radius
diameter
tangent
secant

11. COMMON TANGENTS: A line, ray or segment that is TANGENT to two circles.

12. PRACTICE:
4 COMMON
TANGENTS
3 COMMON
TANGENTS
2 COMMON
TANGENTS

13. PRACTICE:
2 COMMON
TANGENTS
1 COMMON
TANGENT
0 COMMON
TANGENTS

14. PROPERTY OF TANGENTS (1):
Tangents are always perpendicular to the radius of a circle.
Check for tangents using Pythagorean Theorem.
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑙𝑒𝑔
𝑙𝑒𝑔

15. EXAMPLE: In the diagram, 𝑃𝑇 is the radius of ⊙𝑃. Is 𝑆𝑇 tangent to ⊙𝑃?
Use Pythagorean Theorem to verify right angle:
𝑙𝑒𝑔 2 + 𝑙𝑒𝑔 2 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 2
= ???
= ???
𝟏𝟑𝟔𝟗=𝟏𝟑𝟔𝟗
𝑺𝑻 𝒊𝒔 𝒕𝒂𝒏𝒈𝒆𝒏𝒕 𝒕𝒐 ʘ𝑷
Because it is perpendicular to the radius!
YES!

16. PRACTICE: Determine whether 𝐴𝐵 is tangent to ⊙𝐶?14
Use Pythagorean Theorem to verify right angle:
𝑙𝑒𝑔 2 + 𝑙𝑒𝑔 2 = ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 2
= ???
25+144= ???
𝟏𝟔𝟗=𝟏𝟗𝟔
𝑨𝑩 𝒊𝒔 𝑵𝑶𝑻 𝒕𝒂𝒏𝒈𝒆𝒏𝒕 𝒕𝒐 ʘ𝐂
Because it is NOT perpendicular to the radius!
NO!

17. PROPERTY OF TANGENTS (2):
Tangent segments from a common external point are congruent. 𝑆 𝑅 𝑇
𝑅𝑆 ≅ 𝑅𝑇

18. EXAMPLE: 𝐴𝐵 is tangent to ⊙𝐶 at 𝐴 and 𝐴𝐷 is tangent to ⊙𝐶
at 𝐷. Find the value of 𝑥.
Tangent segments are congruent 𝐴𝐵 ≅ 𝐴𝐷
Substitute known values 𝑥 2 +8𝑥−17=8𝑥+15
Subtract − 8𝑥 − 8𝑥
2 𝑥 2 −17=15
Add
2 𝑥 2 =32
Divide
𝑥 2 =16
Square root 𝑥 2 = 16
𝒙=𝟒

19. PRACTICE: 𝐴𝐵 is tangent to ⊙𝐶 at 𝐴 and 𝐴𝐷 is tangent to ⊙𝐶 at 𝐷
PRACTICE: 𝐴𝐵 is tangent to ⊙𝐶 at 𝐴 and 𝐴𝐷 is tangent to ⊙𝐶 at 𝐷. Find the value of 𝑥.
Tangent segments are congruent 𝐴𝐵 ≅ 𝐴𝐷
Substitute known values 𝑥−4=3𝑥+6
Subtract − 3𝑥 − 3𝑥
2𝑥−4=6
Add
2𝑥=10
Divide
𝒙=𝟓

20. HOMEWORK #1:
Pg.655: 3-20, 24-26, 30