AB, CDare the parallel lines drawn in the circle with centre O.If the area of
the green triangle is 10 then what is the area of the triangle OAB?
Answers
Step-by-step explanation:
Radius of bigger circle r
1
=OA=7
Radius of smaller circle r
2
=
2
r
1
=
2
7
Area of the bigger circle C
1
=πr
1
2
=
7
22
×7×7
=154cm
2
Area of the semicircle =
2
154
cm
2
=77cm
2
Area of the smaller circle C
2
=πr
2
2
=
7
22
×
2
7
×
2
7
=
2
77
Area of the unshaded triangle △ABC=
2
1
×AB×OC
=
2
1
×14×7
=49cm
2
∴ Area of the shaded portion =Area of the smaller circle +(Area of semicircle -Area of the triangle △ABC)
=
2
77
+(77−49)
=66.5cm
2