UPSC 2014 CDS I Math Paper

In right ΔOBD, ∠OBD = 30°
Also,BD=CD=

x

2

units
Remember: Perpendicular from the centre to the chord bisects the chord
tan‌30∘=‌‌

OD

BD

⇒‌‌

1

√3

=‌‌

OD

(‌‌ x 2 )

⇒OD=

x

2√3

Also,
cos‌30°=

BD

OB

⇒

√3

2

=

( x 2 )

OB

⇒OB=

x

√3

∴‌‌

‌Radius of circumcircle‌

‌Radius of incircle‌

=‌‌

OB

OD

=

( x √3 )

( x 2√3 )

=2
Thus, the ratio of the radius of circumcircle to that of the incircle is 2 : 1.