Question

In circle O, AP = √10, PB = x and BC = 3. Find the value of x.

Answer 1

The value of x is
`2\ units`

Explanation:

we know that

Applying the tangent-secant theorem

`AP^(2)=PB*PC`

substitute the values and solve for x

`√(10)^(2)=x*(x+3)`

`10=x^(2)+3x`

`x^(2)+3x-10=0`

using a graphing tool

to solve the quadratic equation

The solution is
`x=2\ units`

see the attached figure