Question

Prove that AB is tangent to circle

Answer 1

See Explanation

Explanation:

`AB^2 +OB^2 = 4^2 +3^2 = 16 + 9 =25`

.....(1)

`OA^2 = 5^2 = 25`

..... (2)

From equations (1) & (2)

`AB^2 +OB^2 = OA^2`

Therefore, by converse of Pythagoras theorem, triangle ABO is right angled triangle right angle at B.

Therefore,

Radius OB is perpendicular to AB.

Hence, AB is tangent to the circle with center O at point B.