Question

Geometry SPECIAL SEGMENTS

Answer 1

Explanation:

1). By the theorem for the length of the segments of the intersecting chords in a circle,

`x* 2 = 3* 6`

x = 9

2). By the theorem of secants intersecting outside a circle,

4 × 9 = x × 12

x =
`(36)/(12)`

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,

`2* x = 4* 3`

x = 6