Question

If I draw two circles of radius 3 cm and 5 cm with common centre and draw a line AB such that it is chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.

• A. 2, 2.35
• B. 2.35, 2
• C. 3, 2
• D. 2.16, 2.35

Answer 1

The correct option is A

2, 2.35

CD = 4.46 cm

Since $OE\perp CD$

$⟹CE=DE=2.23\text{cm}$.

Apply Pythagoras Theorem in $\Delta OEC$.

${OE}^2+{CE}^2={OC}^2$

${OE}^2+{2.23}^2=9$

$\therefore {OE}^2=4$

$\Rightarrow OE=2$

In $\Delta OEA$,

${OE}^2+{AE}^2={OA}^2$

$⟹2^2+{AE}^2=5^2$

$⟹AE=4.58\text{cm}$

AC = AE - CE

= 2.35 cm