Properties of circle

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

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

circle

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,

circle

4.

circle

PA × PB = PC × PD

5.

circle

PT^{2}=PA\,\times\,PB

6.

circle

If AB || CD
then ∠EOF = 90°

7.

circle

∠1 = ∠2

8.

circle

∠ACB = 90°

9.

AB + CD = AC + BD
Area of circle= \sqrt{abcd}

10. AB = CD = Direct Common tangent

circle

AB = CD = \sqrt{d^{2}-\left ( r_{{1}}-r_{{2}} \right )^{2}}

11.  AB = CD Transverse Common Tangents

circle

\frac{OP}{ O^{1}P}=\frac{r_{{1}}}{ r^{2}}

AB=CD=  \sqrt{d^{2}-\left ( r_{{1}}+r_{{2}} \right )^{2}}

12.

13.

If CD = radius
then ∠CED = 60°

14.

15.

\frac{AP}{PB}=\frac{r_{1}}{r_{2}}

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

\frac{CD}{RD}= \frac{ r_1\,^{2}}{ r_2\,^{2}}

The length of AB = \frac{ 4\times\,Area\,of\,\triangle\,ACD}{d}

17. Common chord of two equal circle after intersection.

AB = 2\times\frac{\sqrt{3}\,r}{2} = \sqrt{3}\,r

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.

 

 

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