  Let ABC be an isosceles triangle, where AB AC. Suppose that M is a pointon the sideAB such that AB- MB = AM2. Suppose also that AM = BC. Prove that the angle ZABC istwice ZBAC. [Hint: Consider the circumcircle O of AMC. Show that BC is tangent to O.Use this to show that ZCMB = ZCBM . You are encouraged to usepropositions from Books 1,2, & 3 from Euclid's Elements.] Draw a picture to help support your proof.

Question help_outlineImage TranscriptioncloseLet ABC be an isosceles triangle, where AB AC. Suppose that M is a point on the side AB such that AB- MB = AM2. Suppose also that AM = BC. Prove that the angle ZABC is twice ZBAC. [Hint: Consider the circumcircle O of AMC. Show that BC is tangent to O. Use this to show that ZCMB = ZCBM . You are encouraged to use propositions from Books 1, 2, & 3 from Euclid's Elements.] Draw a picture to help support your proof. fullscreen
Step 1

Consider the isosceles triangle having sides AB,BC and AC such as AB=AC.On side AB there is a point M such that AM=BC and .Also triangle AMC have a circumcircle O.Write the given data about this triangle:

Step 2

Now draw the triangle based on above information.

Step 3

Condition for tangency of a line can be ex...

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