Answer: Length of AB is 16 cm
Step-by-step explanation:
Given: Diameter of a circle is 20 cm and CE = 4 cm
Now as shown in figure AO, BO, CO are radii
[tex]\text { Radius } =\dfrac{\text {Diameter}}{2} = \dfrac{20}{2} = 10 cm[/tex]
Therefore
AO=BO=CO= 10 cm
Now
[tex]OE = CO- CE \Rightarrow OE= 10 -4 = 6 cm[/tex]
Now in Δ OEB
∠OEB =90°
Therefore by Pythagoras theorem : In a right angle triangle the square of hypotenuse is equal to the sum of square of other two sides.
So we have
[tex]BO^2=BE^2+EO^2\\\\\Rightarrow 10^2= BE^2 +6^2\\\\\Rightarrow BE^2= 100-36\\\\\Rightarrow BE^2 = 64 \\\\\Rightarrow BE= 8 cm[/tex]
Now as we know perpendicular to the chord from the center of a circle bisect the chord.
Therefore
[tex]AB= 2\times BE = 2\times 8=16 cm[/tex]
Hence , the length of AB is 16 cm .
