State True or false and justify your answer:
1. The length of tangent from an external point of a circle is always greater than the circle.
2.If angle between two tangents drawn from any point P to a circle of radius a and centre O is 60 degree, then OP = a root3.
3. IF a chord PQ subtends an angle of 80degree at the centre of a circle, then angle between the tangents at P and Q is also 80 degree.
4.If a number of circles touch a given line segment at a point A, then their centres lie on the perpendicular bisector of PQ.

The length of tangent from an external point of a circle is always greater than the circle.
- False
As it can be smaller than the radius as shown below,



.If angle between two tangents drawn from any point P to a circle of radius a and centre O is 60 degree, then OP = a root3.


As we know that line OP divides the angle APB So,
sin30 = aOPOP=asin30 =2a
So this statement is also false.

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