powerpoint presentation

1. Subtitle

2. The following theorem relates a radius to a tangent.
– If a line is perpendicular to a radius of a circle at its outer end,
then the line is tangent to the circle.
– If a line is tangent to a circle, then it is perpendicular to the
radius at the point of tangency.

4. If two segments from the same exterior point are
tangent to a circle, then they are congruent.

5. Example:
5x -8
5(5) – 8
25 – 8 = 17
3x + 2
3(5) + 2
15 + 2 = 17

6. Example 1. Find mHK.
JK = HK
2x + 5 = 3x – 2
2x – 3x = -2 – 5
-x = -7
x =
−7
−1
x = 7
HK = 3x – 2
= 3(7) – 2
= 21 – 2
= 19

7. Example 2. Find x.
HG = IG
x + 10 = 2x – 1
10 + 1= 2x – x
11 = x
Since HG = IG
x + 10 = 2x – 1
11 + 10 = 2(11) – 1
21 = 22 -1
21 = 21

8. Activity 3. Using the given figure, if the radius is 12, find JG.
Since HG and IG is 21, and the
radius is 12 then,
JG is the hypotenuse in the ∆𝐺𝐻𝐽
HG2 + HJ2 = JG2
212 + 122 = JG2
441 + 144 = JG2
585 = JG2
585 = JG
9 . 65 = JG
3 𝟔𝟓 = JG