geometry

 

Let AB be a diameter of a circle, and let C be a point on the circle such that AC=8 and BC=14 The angle bisector of ACB intersects the circle at point M Find CM.     

 

Angle ACB is subtended by AB, which is a diameter of the circle, therefore is 90^o.     

Pythagoras' Theorem will determine AB which is the hypotenuse of a right triangle.     

 

AB²  =  AC² + BC²    

AB²  =  8² + 14²  =  260     

AB  =  sqrt(260)     

 

Since CM bisects the 90^o angle subtended by the diameter, it passes

through the center of the circle, thus becoming a diameter itself.     

 

And so, being a diameter . . . CM = sqrt(260)     

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