CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the given figure, lengths of the chords AB and CD are 12 cm and 18 cm respectively and distance between them is 15 cm. Find the radius of the circle.


A

119 cm

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

113 cm

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

117 cm

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

None of these

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

The correct option is C

117 cm


Let the radius of the circle be r.

Given, AB = 12 cm, CD = 18 cm and FE = 15 cm

We know that perpendicular to the chord from the centre bisects the chord.

AF=FB=AB2=6 cm

and CE=ED=CD2=9 cm

Let OE be x cm. Then OF=15x cm.

Applying Pythagoras theorem to AFO,

AO2=AF2+OF2

r2=62+(15x)2 ... (i)

Applying Pythagoras theorem to CEO,

OC2=CE2+OE2

r2=92+x2 ... (ii)

Equating equations (i) and (ii), we get

62+(15x)2=92+x2

36+(15x)2=81+x2

36+225+x230x=81+x2

30x=180

x=18030=6

r2=92+62=117

Radius, r =117 cm.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circles and Their Chords - Theorem 3
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon