Question

The diagram illustrates how the length AB( which cannot be measured directly) of a pond is measured. Choose a point C and measure the length of AC and the length of BC.
Produce AC and BC to A' and B' respectively, so that CA'= AC and CB'= BC. By measuring the length of B'A', we will be able to find the length of AB. why is this so?​

Answer 1

We know that tangent drawn from external point to a circle are equal

So AD=AF=x

Or BD=BE=y

And CF=CE=z

Now, AB=AD+DB=x+y=12 cm ...(1)

Or BC=BE+EC=y+z=8 cm ...(2)

And AC=AF+CF=x+z=10 cm ...(3)

Adding the above three equation, we get

2(x+y+z)=12+8+10=30 cm

Or x+y+z=15 cm

As per equation (1),

x+y=12 cm

Then, z=15−10=5 cm =CF

As per equation (3),

x+z=12 cm

Then, y=15−12=3 cm =BE

As per equation (2),

y+z=8 cm

Then, x=15−8=7 cm =AD