Question

In the figure, 'O' is the centre of the circle. OM = 3 cm and AB = 8 cm. Find the radius of the circle.

• A. $4cm$
• B. $15cm$
• C. $8cm$
• D. $5cm$

Answer 1

Answer: (D)

Given o is the center of circle ,OM=3 cm and AB=8 cm

Join O to A and B

In figure OM show that the perpendicular from center O on cord AB

WE know that Perpendicular from the Center of a Circle to a Chord Bisects the Chord.

Then AM=BM

So $AM=BM=\frac{AB}{2}=\frac{8}{2}=4cm$

$\Delta AOM$

$(AO{)}^2=(AM{)}^2+(OM{)}^2=(4{)}^2+(3{)}^2=16+9=25$

$\Rightarrow AO=5cm$

Then AO is the radius of circle is 5 cm