UPSC CDS 1 2022 Math Paper

Given:
Radius =25cm
Length of chord =48cm
Concept used:
The perpendicular from the center of a circle to a chord bisects the chord.
Pythagoras Theorem: Hypotenuse ‌2= Base 2+ Perpendicular ‌2
Calculation:OA=OB=25cm (Radius of circle)
AB=48cm
PB=AB∕2=48∕2
Using the above concept
PA=PB=24cm
Applying Pythagoras theorem in △OPB ,
OB2=OP2+PB2
⇒252=OP2+242
⇒OP2=625−576
⇒OP2=49
⇒OP=7cm
∴ The length of perpendicular drawn from the centre of the circle to the chord is 7cm .