IB Math SL Portfolio The aim of this task is to investigate positions of points in intersecting circles.

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Aim: The aim of this task is to investigate positions of points in intersecting circles.

Let r = 1. Use an analytic approach to find OP’ when

Radius equals 1; OP is equal to 2, so the other side length must be equal to 2 because this is an isosceles triangle.

Use Law of Cosines To Find Angle:

Cos O =        ------  Where A= 2, O = 2, P = 1.    Where A=A, B=O, C=P  

        

Cosine O=          O=

O = 75. 522 Degrees

Use Law of Sines to Find Other Angles:

      SO                

               

Sin A= .9682

A=                             A= 75.522 degrees

Sum of Triangle = 180 degrees                     Where x is the angle measurement of P

75.522 + x degrees = 180

151.044 + x degrees = 180

151.044-151.044 + x degrees = 180 – 151.044

x degrees = 28. 956

P = 28.956

The angle and side length of A and O are the same. This makes perfect sense because the triangle is an isosceles and since A and O have the same side length, it makes perfect sense that they have the same angle measurement. Hence the sum of the angles of A and O has to be greater than P.

Angle Measurement:

A= 75.522 degrees

O= 75.522 degrees

P= 28.956 degrees

Radius equals 1, OP is equal to 3, so the other side length must be equal to 3 because this is an isosceles triangle.

Use Law of Cosines To Find Angle:

Cos O =        ------  Where A= 3, O = 3, P = 1.    Where A=A, B=O, C=P  

        

Cosine O=          O=

O = 83.621 Degrees

Use Law of Sines to Find Other Angles:

      SO                

               

Sin A= .9994

A=                             A= 83.621 degrees

Sum of Triangle = 180 degrees                     Where x is the angle measurement of P

83.621 + x degrees = 180

167.242 + x degrees = 180

167.242 - 167.242 + x degrees = 180 – 167.242

x degrees = 12.956

P = 12.956 degrees

The angle and side length of A and O are the same. This makes perfect sense because the triangle is an isosceles and since A and O have the same side length, it makes perfect sense that they have the same angle measurement. Hence the sum of the angles of A and O has to be greater than P.

Angle Measurement:

A= 83.621 degrees

O= 83.621 degrees

P= 12.956 degrees

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Radius equals 1, OP is equal to 4, so the other side length must be equal to 4 because this is an isosceles triangle.

Use Law of Cosines To Find Angle:

Cos O =        ------  Where A= 4, O = 4, P = 1.    Where A=A, B=O, C=P  

        

Cosine O=          O=

O = 86.417 Degrees

Use Law of Sines to Find Other Angles:

      SO                

               

Sin ...

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