Question

If $OA=5$ cm, $AB=8$ cm and $OD$ is perpendicular to $AB$, then $CD$ is equal to:

• A. $2$ cm
• B. $3$ cm
• C. $4$ cm
• D. $5$ cm

Answer 1

Answer: (A)

$2$ cm

Given, $OA=5$ cm, $AB=8$ cm

And $OD$ is perpendicular to $AB,$ so $AC=CB=8/2=4cm$

In triangle $ACO,$

$A{O}^2=A{C}^2+C{O}^2$, by using pythagoras theorem, we get

$25=16+C{O}^2$

$CO=3$ cm

$OD=$ radius $=5$cm

$CD=OD-OC=5-3=2$ cm