Two circles of radii 5 cm and 6 cm with common centre are drawn. There is a line AB such that it is chord to both the circles. CD=8 cm. Find the distance of the chord from centre and the length of AC respectively.
2, 2.35
Given, CD=8 cm
Since, OE⊥CD
⇒CE=DE=CD2=4 cm.
Applying Pythagoras Theorem in ΔOEC.
OE2+CE2=OC2
⇒OE2+42=52
∴OE2=25−16
⇒OE=3 cm
In ΔOEA,
OE2+AE2=OA2
⇒32+AE2=62
⇒AE2=36−9=27
⇒AE=√27=3√3=3×1.73=5.19 cm
Now, AC=AE−CE=5.19−4=1.19 cm