AB is the diameter of a circle and AC is a chord of length 6 cm. If the radius of the circle is 5 cm then the length of BC is i)6 cm ii)8 cm iii)10 cm iv)4 cm
Answers
Answered by
0
Answer:
i 6 is answer
Step-by-step explanation:
Answered by
1
Step-by-step explanation:
Correct option is
A
54.5 cm
2
Given:
AB is the diameter =d of a circle.
ΔABC has the diameter AB as base & the point C is on the circumference.
AC=6 cm and BC=8 cm.
To find out:
Area of shaded portion in the given circle.
Solution:
∠ACB=90
o
since ΔABC has been inscribed in a semicircle.
∴ΔABC is a right one with AB as hypotenuse ...(i)
So, applying Pythagoras theorem, we have
AB=
(AC)
2
+(BC)
2
=
(6)
2
+(8)
2
cm=10 cm=d.
∴ The radius of the given circle =
2
d
=
2
10
cm=5 cm.
i.e The Area of circle =πr
2
=3.14×5
2
cm
2
=78.5cm
2
.
Again, Area of ΔABC=
2
1
×AC×BC (by i)
=
2
1
×6×8cm
2
=24cm
2
.
Now, Area of shaded region = Area of circle − area of ΔABC
=(78.5−24)cm
2
=54.5cm
2
.
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