https://artofproblemsolving.com/wiki/index.php?title=1986_AHSME_Problems/Problem_3&feed=atom&action=history
1986 AHSME Problems/Problem 3 - Revision history
2024-03-28T18:25:14Z
Revision history for this page on the wiki
MediaWiki 1.31.1
https://artofproblemsolving.com/wiki/index.php?title=1986_AHSME_Problems/Problem_3&diff=93687&oldid=prev
Hapaxoromenon: Fixed the problem statement and added a solution with explanation
2018-04-01T22:03:58Z
<p>Fixed the problem statement and added a solution with explanation</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 22:03, 1 April 2018</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Problem==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Problem==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\triangle ABC</math> <del class="diffchange diffchange-inline">is </del>a right angle at <math>C</math> and <math>\angle A = 20^\circ</math>. If <math>BD</math> (<math>D</math> in <math>\overline{AC}</math>) is the bisector of <math>\angle ABC</math>, then <math>\angle BDC =</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\triangle ABC</math> <ins class="diffchange diffchange-inline">has </ins>a right angle at <math>C</math> and <math>\angle A = 20^\circ</math>. If <math>BD</math> (<math>D</math> in <math>\overline{AC}</math>) is the bisector of <math>\angle ABC</math>, then <math>\angle BDC =</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>\textbf{(A)}\ 40^\circ \qquad</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>\textbf{(A)}\ 40^\circ \qquad</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Solution==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Since <math>\angle C = 90^{\circ}</math> and <math>\angle A = 20^{\circ}</math>, we have <math>\angle ABC = 70^{\circ}</math>. Thus <math>\angle DBC = 35^{\circ}</math>. It follows that <math>\angle BDC = 90^{\circ} - 35^{\circ} = 55^{\circ}</math>, which is <math>\boxed{D}</math>.</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
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Hapaxoromenon
https://artofproblemsolving.com/wiki/index.php?title=1986_AHSME_Problems/Problem_3&diff=65731&oldid=prev
Timneh: /* See also */
2014-10-24T06:29:14Z
<p><span dir="auto"><span class="autocomment">See also</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 06:29, 24 October 2014</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{AHSME box|year=1986|<del class="diffchange diffchange-inline">before=</del>num-b=2|num-a=4}}   </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{AHSME box|year=1986|num-b=2|num-a=4}}   </div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Introductory Geometry Problems]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category: Introductory Geometry Problems]]</div></td></tr>
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Timneh
https://artofproblemsolving.com/wiki/index.php?title=1986_AHSME_Problems/Problem_3&diff=65730&oldid=prev
Timneh: Created page with "==Problem== <math>\triangle ABC</math> is a right angle at <math>C</math> and <math>\angle A = 20^\circ</math>. If <math>BD</math> (<math>D</math> in <math>\overline{AC}</math>)..."
2014-10-24T06:28:56Z
<p>Created page with "==Problem== <math>\triangle ABC</math> is a right angle at <math>C</math> and <math>\angle A = 20^\circ</math>. If <math>BD</math> (<math>D</math> in <math>\overline{AC}</math>)..."</p>
<p><b>New page</b></p><div>==Problem==<br />
<br />
<math>\triangle ABC</math> is a right angle at <math>C</math> and <math>\angle A = 20^\circ</math>. If <math>BD</math> (<math>D</math> in <math>\overline{AC}</math>) is the bisector of <math>\angle ABC</math>, then <math>\angle BDC =</math><br />
<br />
<math>\textbf{(A)}\ 40^\circ \qquad<br />
\textbf{(B)}\ 45^\circ \qquad<br />
\textbf{(C)}\ 50^\circ \qquad<br />
\textbf{(D)}\ 55^\circ\qquad<br />
\textbf{(E)}\ 60^\circ</math> <br />
<br />
==Solution==<br />
<br />
<br />
== See also ==<br />
{{AHSME box|year=1986|before=num-b=2|num-a=4}} <br />
<br />
[[Category: Introductory Geometry Problems]]<br />
{{MAA Notice}}</div>
Timneh