8. Two parallel chords AB and CD are 3.9 cm apart and lie on the opposite sides of the centre
of a circle. If AB = 1.4 cm and CD = 4 cm, find the radius of the circle.
Answers
Step-by-step explanation:
copy little bit from photo.
cf=fd=1/2 cd same reason
cf = fd = 1/2 × 4
cf = fd = 2
let oe be x
oe=x
ef=eo+of
3.9 = x+of
of=3.9-x
ao = co radii of same circle .......1
In triangle AEO m angle AEO = 90 .....2
In triangle OFC m angle OFC = 90 ......3
from 1 2 and 3
\begin{gathered}{ae}^{2} + {eo}^{2} = {of}^{2} + {fc}^{2} \\ {0.7 }^{2} + {x}^{2} = (3.9 - {x}^{2}) + {2}^{2} \\ 0.49 + {x}^{2} = {x}^{2} - 7.8x + 15.21 + 4 \\ 7.8x = 18.72 \\ x = \frac{18.72}{7.8 } \\ x = 2.4cm\end{gathered}
ae
2
+eo
2
=of
2
+fc
2
0.7
2
+x
2
=(3.9−x
2
)+2
2
0.49+x
2
=x
2
−7.8x+15.21+4
7.8x=18.72
x=
7.8
18.72
x=2.4cm
ao^2=ae^2+oe^2
ao^2=
\begin{gathered}{0.7}^{2} + {2.4 }^{2} \\ 0.49 + 5.76 \\ 6.25 \\ \sqrt{6.25 } \\ 2.5\end{gathered}
0.7
2
+2.4
2
0.49+5.76
6.25
6.25
2.5
radius of circle is 2.5 cm.
