The problem comes from the textbook, Kiselev's Geometry. Book I. Planimetry by A. P. Kiselev:Prove theorem: To two circles tangent externally at a point A, a common external tangent BC is drawn(where B and C are the tangency points). Prove that the angle BAC is right. Hint: Draw through A a common tangent and examine the triangles ABD and ADC.

Answered: Prove theorem: To two circles tangent…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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The problem comes from the textbook, Kiselev's Geometry. Book I. Planimetry by A. P. Kiselev:

Prove theorem: To two circles tangent externally at a point A, a common external tangent BC is drawn(where B and C are the tangency points). Prove that the angle BAC is right.

Hint: Draw through A a common tangent and examine the triangles ABD and ADC.

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According to given problem,

To prove,

∠BAC is right ⇒∠BAC=90°

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