a diameter AB of a circle is perpendicular to the chord CD at point 5. CD equals to 20cm AX equals 8cm.what is the length of the diameter
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From the above diagram
AB=diameter
CD= chord
Cx=XD=10cm
XA=8CM
CO= RADIUS (r)
by using Pythagoras theorem
in triangle COX
OX= (r-8)
CO=r
CX=10
CO²=CX²+OX²
r²=(10)²+(r-8)²
r²=100+r²+64-16r. (using (a-b)²)
r² gets cancelled
164-16r=0
164=16r
r=10.25
d=2r
d=2*10.25
=20.5
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