Question

Find the length of the radius

Answer 1

6

Explanation:

Use the given information combine with the Pythagorean theorem to set up an equation. The Pythagorean theorem states that (
`a^2 + b^2 = c^2`), where (a) and (b) are the legs of the right triangle (sides that are adjacent to the right angle); and (c) is the hypotenuse (the side opposite to the right angle). Substitute in the given values in the problem,

`a^2 + b^2 = c^2`

Substitute,

`QO^2 + QP^2 = PO^2`

`x^2 + 8^2 = (4+x)^2`

Simplify, distribute

`x^2 + 64 = x^2 + 8x + 16`

Inverse operations,

`x^2 + 64 = x^2 + 8x + 16\\-x^2\\\\64 = 8x + 16\\-16\\\\48 = 8x\\/8\\\\6 = x`