# |Let ABC be an isosceles triangle, where AB= AC. Suppose that M is a point on 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 OUse 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.

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125 views help_outlineImage Transcriptionclose|Let 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
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Step 1

To show that (under the given conditions) that angle A = 36 and (hence B=72=2A)

Step 2

We may take AB = AC =1 and AM = BC=x. The given condition yields a quadratic equation for x.

Step 3

Solve for x.&...

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