Area-Circle & Triangle

solution of a triangle

Incentre is concurrence point of angle bisectors of triangle. The three sides of the triangle are tangents to the cirle with centre O.

incentre of a triangle

 Radius of in circle of an equilateral triangle of side a = a/2Ö3

op = oq = or = radius or Inradius and o is incentre

incentre of equvilateral triangle

·  Circum centre is concurrence point of perpendicular bisectors of a triangle.

Circum centre of a triangle

Radius of circum circle of an equilateral triangle of side a = a/Ö3

OP = OQ = OR Þ Circum Radius O is circum centre 

circum circle of equilateral triangle


·                     Relationship between inradius and circumradius:

If r is radius of incircle & R is radius of circumcircle then

A (area of triangle) =  pr = abc/4R

where a, b & c are sides of the triangle and p is semi perimeter of the triangle.

                p = ( a+b+c)/2


area of sector

  Area of circle = ÕR2, where R is the radius of the circle. OP  = R = Radius 

 Circumference of a circle = 2ÕR. This is also known as perimeter of circle.

Length of arc,  is 2Õq/360  where q is the central angle.  

 Are of a sector = Area of sector POQ =   ÕR2q/360

Area of a semi-circle  ÕR2/2.

area of a semi circle

                 Circumference of a semi-circle = ÕR.

                Perimeter of a semicircle is ÕR + 2R