Please help and explain.

Question

asked Apr 18, 2024 204k views

2 Answers

Srborlongan · Answer 1 · 2024-04-24T11:12:00+0000

Answer:

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)