Question

If the diameter of semi circle is AB then,
C is a point on AB such that a perpendicular is drawn from it which intersects the circumference of circle at E. if ac=2 and CE=6 find area of circle bounded; If the diameter of semi circle is AB then,; C is a point on AB such that a perpendicular is drawn from it which intersects the circumference of circle at E. if ac=2 and CE=6 find area of circle bounded

Answer 1

To find area of semi circle

firstly we have to find the length of radius which would denoted as ‘R’

In other words, R = AB/2 which is mid point of AB ,

the mid point can be named as “o” i.e, AO=BO=R

Now AC=2 , & CD =6

Hence CO= (R-2)

If the point ‘O’ and ‘D’ , OD=R, Now right angled triangle CDO

Now using Pythagoras formula, (OD)^2 = (CO)^2 +(CD)^2——-(1)

OD= R, CO= (R-2) and CD=6

Substituting the above in equation (1)

R^2=(R-2)^2 +6^2

R^2= R^2 +4 -4R+36

Now 4R = (36+4)

So, R= 40/4=10

Diameter AB=2R=10x2 =20

Area of Semicircle = (22/7)(20)^2/8=157.08 Sq. Units