In the given figure, OD bisects AB. If AB = 8 cm and the radius of circle is 5 cm, then OD is equal to .

3 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 3 cm
Given: AB = 8 cm and OD bisects AB.
So, AD = DB = 4 cm.

$∠ O D B = 90^{\circ}$ [Line through centre that bisect the chord is perpendicular to chord.]

So, $O B^{2} = O D^{2} + D B^{2}$ [ $∵ Δ$ ODB is right angled triangle.]
$O D^{2} = O B^{2} - D B^{2}$
$O D^{2} = (5)^{2} - (4)^{2}$ [OB is radius]
$O D^{2} = 25 - 16$
$O D^{2} = 9$
OD = 3 cm

Suggest Corrections

Similar questions

Q. In given figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB then CD is equal to

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then find the distance of OD.

Q. In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ___.

Q. In the given figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:

In the circle shown below AB is the chord having length 8 cm and being bisected by the line OD from centre. If the radius of circle is 5 cm, then distance OD is equal to

Join BYJU'S Learning Program

In the given figure, OD bisects AB. If AB = 8 cm and the radius of circle is 5 cm, then OD is equal to .

The correct option is A 3 cmGiven: AB = 8 cm and OD bisects AB. So, AD = DB = 4 cm. ∠ODB=90∘ [Line through centre that bisect the chord is perpendicular to chord.] So, OB2=OD2+DB2 [∵ΔODB is right angled triangle.] OD2=OB2−DB2 OD2=(5)2−(4)2 [OB is radius] OD2=25−16 OD2=9 OD = 3 cm