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let AB be diameter of circle and AC be the chord. Let a tangent is drawn from C to meet AB produced at D.If BAC=30,Prove that BC= BD

SOLUTION

ACB= 90

ABC=60

CBD=120

After that I am confused

rst
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  • 3 theorems you should know. (1) Angles in semi-circle; (2) Angles in alternate segment; (3) Converse of an isosceles triangle. – Mick Nov 14 '14 at 15:58
  • What is an "alternate segment", and what is "the converse of an isosceles triangle"? – Timbuc Nov 14 '14 at 16:03

1 Answers1

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Remember the theorem about the angle between a tangent and a cord at the tangency point, so you get

$$\angle BCD=\angle CAB=30^\circ$$

Using now that $\;\angle CBD=120^\circ\;$, deduce $\;\Delta BCD\;$ is isosceles and you're done.

Timbuc
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  • can u pls suggest a book for elementery geometry ? – godonichia Nov 14 '14 at 16:34
  • @godonichia, I loved Harold Jacobs' "Geometry"...and I read it completely while in graduate school. It is the first one here:http://www.abebooks.com/book-search/title/geometry/author/harold-jacobs/ , though I think there are new editions now. – Timbuc Nov 14 '14 at 16:49