If I draw two circles of radius 3cm and 5cm with common centre and draw a line AB such that it is a chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.
2, 2.35
CD = 4.46cm
Since OE⊥CD
⟹CE=DE=2.23 cm.
Apply Pythagoras Theorem in ΔOEC.
OE2+CE2=OC2
OE2+2.232=9
∴OE2=4
⇒OE=2
In ΔOEA,
OE2+AE2=OA2
⟹22+AE2=52
⟹AE=4.58 cm
AC = AE - CE
= 2.35 cm