Question

In the diagram below NP is tangent to circle O. NP = 20 and OP = x+4. NO = x. Solve for the value of x, and the length of OP.

Answer 1

we know that

applying the Pythagorean theorem
OP²=NO²+NP²
(x+4)²=x²+20²--------> (x²+8x+16)=x²+400-------------> 8x+16=400
8x=384-----------> x=48 units

OP=x+4-------> OP=48+4--------> OP=52 units

the answer is
x=4 units
OP=52 units