Question

If the diameter of circle O is 20 and CE = 4, then determine the length of AB. Show how you arrived at your answer.

Answer 1

Answer: Length of AB is 16 cm

Explanation:

Given: Diameter of a circle is 20 cm and CE = 4 cm

Now as shown in figure AO, BO, CO are radii

`\text { Radius } =\frac{\text {Diameter}}{2} = (20)/(2) = 10 cm`

Therefore

AO=BO=CO= 10 cm

Now

`OE = CO- CE \Rightarrow OE= 10 -4 = 6 cm`

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

`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`

Now as we know perpendicular to the chord from the center of a circle bisect the chord.

Therefore

`AB= 2* BE = 2* 8=16 cm`

Hence , the length of AB is 16 cm .