Question

What’s the correct answer for this question?

Answer 1

19

Explanation:

In the circle with center M, BD is tangent and BA is secant, which are intersecting each other outside of the circle at point B.

BA = BE + EA = 4 + x - 7 = x - 3

Now, by the property of intersecting tangent and secants outside of the circle.

`BD^2 = BE * BA\\</p><p>\therefore 8^2 = 4* (x - 3)\\</p><p>\therefore 64 = 4x - 12</p><p>\therefore 64+12 = 4x\\</p><p>\therefore 76 = 4x\\\\</p><p>\therefore x = (76)/(4)\\\\</p><p>\huge \orange {\boxed {\therefore x = 19}} \\`

Answer 2

x = 19

Explanation:

Using tangent - secant theorem,

(BD)² = (BE)(BA)

(8)² = (4)(4+x-7)

64 = 4(x-3)

64 = 4x - 12

4x = 64+12

4x = 76

Dividing both sides by 4

x = 19