The document discusses common tangents to circles and classifies examples as internally or externally tangent. It also determines whether lines represent internal or external tangents in several examples. The document explains how to use the Pythagorean theorem to find unknown sides of right triangles, providing two examples: finding the length of side BA when DA is 10 and DB is 5, and finding the length of side PA when PO is 5 and AO is 3.

1. Common Tangents

2. A. Classify as externally tangent or internally
tangent circles
1. Internally tangent 2. Externally tangent

3. Classify as externally tangent or internally
tangent circles
3.Externlly tangent 4. Internally tangent

4. B. Determine whether the following lines is an
internal tangent or external tangent.
1. 𝑃𝑄 = external tangent
2. 𝑅𝐶 = internal tangent

5. B. Determine whether the following lines is an
internal tangent or external tangent.
3. 𝑃𝑄 = external tangent
4. 𝑅𝐹 = external tangent
5. 𝐸𝐹 = internal tangent

6. B. Determine whether the following lines is an
internal tangent or external tangent.
6. 𝐴𝐵 = external tangent
7. 𝐶𝐷 = external tangent
8. 𝐸𝐹 = internal tangent
9. 𝐻𝐺 = internal tangent

7. C. Give what is being asked.
1. Let 𝐷𝐴 = 10. If 𝐷𝐵 is 5, find 𝐵𝐴or (r) .
Pythagorean Theorem
The Pythagoras theorem is a mathematical
law that states that the sum of squares of the
lengths of the two short sides of the right triangle
is equal to the square of the length of the
hypotenuse.

8. c
a
b
1. 𝐷𝐴 (c) = 10.
𝐷𝐵 (b) = 5
𝐵𝐴 (a)= ?
a2 + b2 = c2
𝐵𝐴2
+ 𝐷𝐵2
= 𝐷𝐴2
(BA)2 + 52 = 102
(BA)2 + 25 = 100
(BA)2 = 100 – 25
(BA)2 = 75
BA = 75
BA = 25 . 3
BA = 5 𝟑
Solution:

9. 2. Let PO = 5, AO = 3. Find PA.
Solution:
(PA)2 + (AO)2 = (PO)2
(PA)2 + 32 = 52
(PA)2 + 9 = 25
(PA)2 = 25 – 9
(PA)2 = 16
PA = 16
PA = 4