<p>Hello there, this one has stumped me:</p>
<p>In the figure in the link above, line segments BD and AB are tangent to the circle at points C and A, respectively. If the circle is centered at E, what angle must have the same measure as <ABD? </p>
<p>(A) <BAD
(B) <BCE
(C) <CDE
(D) <CEA
(E) <CED</p>
<p>The answer is <CED, but could someone please offer an explanation of why?</p>
<p>Thanks!</p>
<p><ABD + <CEA = 360
<CED + <CEA = 360
So <ABD = <CED</p>
<p>Sorry I mean 180 not 360</p>
<p><ABD + <CEA = 180
<CED + <CEA = 180
So <ABD = <CED</p>
<p>Thanks for responding. :)</p>
<p>Ok, so I get the first part, but how do you know: <ABD + <CEA = 180 ??</p>
<p>It’s <CED because triangles ABD and CED are similar triangles. This is because they are both right triangles (<ECD and <BAD) and share the angle <ADB, so they are congruent for all the angles.</p>
<p><ECD = 90° (tangent)
<DAB = 90° (tangent)</p>
<p>Look at the triangle ADB and then compare it to the triangle CDE. Both have one right angle and use the same angle at point D -> therefore, <ABD = <CED.
Consequently: <ABD + CEA = 180°</p>
<p>Awww, I get it now! Thanks a bunch guys! :)</p>
