UPSC CDS I 2025 Mathematics Paper

Given:
C is the center of a circle with radius =20cm.
AB is a chord of length =32cm.
CE=13cm,E is a point on AB .
We need to find AE×EB.
Formula used:
In a circle, for any chord AB and point E on AB :
AE×EB=(. Radius 2− Distance from center to chord ‌2)
Calculation:
Radius =20cm, so Radius 2=202=400
Distance from center to chord (CE)=13cm, so CE2=132=169
⇒AE×EB= Radius 2−CE2
⇒AE×EB=400−169
⇒AE×EB=231