Question

In the given fig. AP is tangent to circle at A. Find the value of X?

Answer 1

See the attached file

Answer 2

AP is perpendicular to AO { according to the therom that angle between tangent and radius is 90 degree}

so by Pythagoras therom ,

(x+2)^2 =(x+1)^2 + 3^2

x^2+4x+4 = x^2+2x+1+9

{x^2 will get canceled }

4x+4=2x+10

4x-2x=10-4

2x=6

x=3.

the sides are : -
AP=(x+1)
     =4

OP = (X+2)
       = 5

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