Respuesta :

Answer:

24

Step-by-step explanation:

Objective: Circle Theorems. Understand that if two tangents of a circle are tangent to the same point, they are equal.

Using that this means that

DB equal CB.

[tex]5x + 20 = 10x + 16[/tex]

[tex]20 = 5x + 16[/tex]

[tex]4 = 5x[/tex]

[tex]x = \frac{4}{5} [/tex]

Plug in line CB, 5x+20 to find the answer.

[tex]5( \frac{4}{5} ) + 20 = 24[/tex]

The length of the tangent BC will be 24 units. Then the correct option is A.

What is a circle?

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The tangent BD = 10x + 16 and BC = 5x + 20.

If the tangents are drawn from a point outside the circle. Then the length of the tangents will be equal. Then we have

BD  = BC

10x + 16 = 5x + 20

5x = 4

x = 0.8

Then the length of the tangent BC will be

BC = 5(0.8) + 20

BC = 4 + 20

BC = 24 units

Then the correct option is A.

More about the circle link is given below.

https://brainly.com/question/11833983

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