Question

Please help and explain.​

Answer 1

Please brain-list would be appreciated

Answer 2

R = 13 cm, x = 5 cm

Explanation:

We can see, that AO = BO = EO

First, we have to find AO from ∆OAD by using the Pythagorean theorem:

`{ao}^(2) = {ad}^(2) + {x}^(2)`

`{ao}^(2) = 144 + {x}^(2)`

`ao > 0`

`ao = \sqrt{144 + {x}^(2) }`

Now, let's write that EO = (8 + x)

Since AO = EO, we can write an equation:

`\sqrt{144 + {x}^(2) } = 8 + x`

Let's square the whole equation:

`144 + {x}^(2) = ( {8 + x})^(2)`

`144 + {x}^(2) = 64 + 16x + {x}^(2)`

`{x}^(2) - {x}^(2) - 16x = 64 - 144`

`- 16x = - 80`

Let's divide both sides of the equation from -16:

`x = 5`

OB = 8 + x = 8 + 5 = 13 (radius)