Question

In given figure, 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

The correct option is A 2 cm

OC is perpendicular on chord AB

$\therefore OC$ bisects the chord AB

$\Rightarrow AC=CB$

Now,

$AC+CB=AB$

$\Rightarrow AC+CB=8$

$\Rightarrow AC=\frac{8}{2}$

$\Rightarrow 4$cm

$△OCA$ is a right angled triangle

$\therefore A{O}^2=A{C}^2+O{C}^2$

$\Rightarrow 5^2=4^2+O{C}^2$

$\Rightarrow 5^2-4^2=O{C}^2$

$\Rightarrow O{C}^2=9$

$\Rightarrow OC=3$

Since, OD is the radius of the circle

$\therefore OA=OD=5$cm

$CD=OD-OC$

$\Rightarrow 5-3=2$cm