Answer:
Step-by-step explanation:
1). By the theorem for the length of the segments of the intersecting chords in a circle,
[tex]x\times 2 = 3\times 6[/tex]
x = 9
2). By the theorem of secants intersecting outside a circle,
4 × 9 = x × 12
x = [tex]\frac{36}{12}[/tex]
x = 3
3). By the theorem of secant and tangent intersecting outside a circle,
x² = 2(2 + 6)
x² = 16
4). By the theorem of secant and tangent intersecting outside a circle,
6² = 3x
3x = 36
x = 12
5). By the theorem for the length of the segments of the intersecting chords in a circle,
[tex]2\times x = 4\times 3[/tex]
x = 6
