Question

In the following figure find x​

Answer 1

Answer:

OA is perpendicular to AP

OA is perpendicular to AP => <A = 90°

{ Reason :

Tangent at the point of contact is perpendicular to the radius of the circle .}

In ∆ AOP,

PO² = AO² + AP² { Pythagoras theorem }

( x + 1 )² = x² + ( x - 1 )²

x² + 2x + 1 = x² + x² - 2x + 1

x² + 2x +1 = 2x² - 2x + 1

2x² - x² -2x - 2x + 1 - 1 = 0

x² - 4x = 0

x ( x - 4 ) = 0

[ x = 0 & x - 4 = 0]

=> [ x = 0 & x = 4 ]

hope it helps you