In the diagram, AB and DB are tangents to the circle with centre O and radius 9cm. If angle ABD = 75 degrees, calculate the area of the shaded region.
FYI, angle AOD is 105 degrees.
Here's the diagram:
http://www.flickr.com/photos/13256126@N0…
FYI, angle AOD is 105 degrees.
Here's the diagram:
http://www.flickr.com/photos/13256126@N0…
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Connect point B to O, line BO bisects angles ABD & AOD: the right triangles AOB and DOB are congruent:
tan(105/2) = BD/9
BD = AB = 11.73 cm
Area of DOB + AOB:
= 2(1/2 * 9 * 11.73) = 105.56 cm^2
Area of the sector of a circle:
A = C/360 * pi * r^2
for OAD:
A = 105/360 * pi * 81 = 74.22 cm^2
Area of the shaded part:
A = 105.56 - 74.22 = 31.34 cm^2
tan(105/2) = BD/9
BD = AB = 11.73 cm
Area of DOB + AOB:
= 2(1/2 * 9 * 11.73) = 105.56 cm^2
Area of the sector of a circle:
A = C/360 * pi * r^2
for OAD:
A = 105/360 * pi * 81 = 74.22 cm^2
Area of the shaded part:
A = 105.56 - 74.22 = 31.34 cm^2
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You are welcome, thanks & Regards.
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