Answer:
THEOREMS
Intersecting Secants Theorem
If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
Intersecting chords theorem
The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
Tangent-secant theorem
If a secant and a tangent of a circle are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment.
1.
2m = 3(4)
2m = 12
2m/2 = 12/2
m = 2
2.
6(n+2) = 8(3)
6n + 12 = 24
6n = 24 - 12
6n = 12
6n/6 = 12/6
n = 2
3.
4 (n+4) = 8^2
4n + 16 = 64
4n = 64 - 16
4n = 48
4n/4 = 48/4
n = 12
m (m + 12) = 8^2
m^2 + 12m = 64
m^2 + 12m - 64 = 0
(m + 16) (m - 4) = 0
m - 4 = 0
m = 4
4.
9( m +9) = 12 (12 +18)
9m + 81 = 12(30)
9m + 81 = 360
9m = 360 - 81
9m = 279
9m/9 = 279/9
m = 31
5.
32x = 6(6 +18)
32x = 6(24)
32x = 144
32x/32 = 144/32
x = 9/2
x = 4.5
