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junior college 2 | H2 Maths
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Hi im unsure about how to do this, does anyone know how? Help is much appreciated!
Date Posted: 6 years ago
Views: 479
Same method as before. Find the segment of one circle after adding the chord AB.
Now that the circles are the identical, so you just need to find the area of two segments (i.e multiply by 2)
Now that the circles are the identical, so you just need to find the area of two segments (i.e multiply by 2)
Okay ill try that out! Thanks!
Hi i cant get the ans. Could you explain about the method a bit more? Thanks!
Let D be the midpoint of the chord AB.
Let the centre of the left circle be O.
You know that the radius of each circle is 4 cm.
Notice that if you draw a line from the centre of the left circle (point O) to the centre of the right circle, you would just obtain the radius (4cm)
OD is half of that . OD = 2 cm.
Now since OA is also a radius of the cricle , OA = 4 cm. Now, use trigo to find angle AOD.
Angle AOB is just twice of that since angle AOD and angle BOD are the same.
Having found angle AOB, find area of the sector AOB. Then, find area of the triangle AOB. (Use Pythagoras theorem to find AD)
Subtract these two areas from the circle to get the segment.
Let the centre of the left circle be O.
You know that the radius of each circle is 4 cm.
Notice that if you draw a line from the centre of the left circle (point O) to the centre of the right circle, you would just obtain the radius (4cm)
OD is half of that . OD = 2 cm.
Now since OA is also a radius of the cricle , OA = 4 cm. Now, use trigo to find angle AOD.
Angle AOB is just twice of that since angle AOD and angle BOD are the same.
Having found angle AOB, find area of the sector AOB. Then, find area of the triangle AOB. (Use Pythagoras theorem to find AD)
Subtract these two areas from the circle to get the segment.
Okay thank you!
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Always spot for ways to form right angle triangles with derivable or known length of sides.
Chord AB splits QR into half, as both are circles with same radius. Hence, QR is 4cm, and QS is 1/2 of 4cm.
AQ is 4cm, the radius of circle. From here, you can work out AS with a² + b²= c². which will be Sqrt of 12.
Here on, you can find angle AQS, then multiply by 2 to get angle AQB.
From this point on, you can apply the area of segment formula minus the area of triangle, then x 2 to find area of shaded part.
Chord AB splits QR into half, as both are circles with same radius. Hence, QR is 4cm, and QS is 1/2 of 4cm.
AQ is 4cm, the radius of circle. From here, you can work out AS with a² + b²= c². which will be Sqrt of 12.
Here on, you can find angle AQS, then multiply by 2 to get angle AQB.
From this point on, you can apply the area of segment formula minus the area of triangle, then x 2 to find area of shaded part.
Date Posted:
6 years ago
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