Question

I drew two circles of radius 3cm and 5cm with the common centre. Line AB is the chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from the 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 = 4.46cm

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 $\Delta OEA$,

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

$⟹2^2+{AE}^2=5^2$

$⟹AE=4.58\text{cm}$

$AC=AE-CE$

$=2.35cm$