# Properties of circle

1. A tangent at any point of circle is Perpendicular to the radius through the point of contact.

2. The lengths of two tangents, drawn from an external point to a circle, are equal.

AP = AQ

∠P + ∠O = 180°

PO is angle bisector of ∠P & ∠O

3. If two chords AB and CD are crossing each other at a center P then,

4.

PA × PB = PC × PD

5.

6.

If AB || CD

then ∠EOF = 90°

7.

∠1 = ∠2

8.

∠ACB = 90°

9.

AB + CD = AC + BD

Area of circle=

10. AB = CD = Direct Common tangent

AB = CD =

11. AB = CD Transverse Common Tangents

12.

13.

If CD = radius

then ∠CED = 60°

14.

15.

16. if CD is perpendicular bisector of the common chord AB ,then

The length of AB =

17. Common chord of two equal circle after intersection.

AB = =

18.

(a) If any trapezium ABCD, where AB || CD, is inscribed is a circle, Then its non-parallel sides (i.e AC and BD), are equal and AD = BC.