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Let AB be a diameter of a circle.  Let C and D be points on the circle, on opposite sides of diameter AB.  If OA = 5, and BC = 6, then find tan angle BDC.

 May 19, 2020
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Let AB be a diameter of a circle.  Let C and D be points on the circle, on opposite sides of diameter AB.  If OA = 5, and BC = 6, then find tan angle BDC.

 

AB = 10

 

BC = 6

 

If C and D are on opposite sides on a circle (180º apart from each other), then AD = 6

 

BC is one leg of the right triangle, line segment CD (diameter) is the hypotenuse, and BD is the second leg.

 

CD = 2 * OA = 10

 

Let angle BDC be β                 sin(β) = BC / CD

 

                                                 β = 36.86989765º smiley

 May 20, 2020

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