RMO 1998 Geometry

Geometry Level 3

Let A B C D ABCD be a convex quadrilateral in which ∠ B A C = 5 0 ∘ , ∠ C A D = 6 0 ∘ , ∠ C B D = 3 0 ∘ \angle BAC = 50^{\circ}, \angle CAD = 60^{\circ}, \angle CBD = 30^{\circ} and ∠ B D C = 2 5 ∘ \angle BDC = 25^{\circ} . If E E is the point of intersection of A C AC and B D BD , find ∠ A E B \angle AEB .


The answer is 95.

Shashank Rammoorthy by Shashank Rammoorthy , 20, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Ahmad Saad
Dec 26, 2015

5 Helpful 1 Interesting 1 Brilliant 0 Confused

By what test of congruence are triangles GJC and GKD congruent??

Sachin Gadkar - 2 years, 3 months ago
Himanshu Singh
May 28, 2016

Observe that A is the center of a circle that passes through B C D (because of angle values)

2 Helpful 0 Interesting 1 Brilliant 0 Confused
Reetun Maiti
Dec 4, 2015

Mark a point Z such that Angle CZE is equal to 30 degrees. Join ZD. Quad ABZD is cyclic. Again C is the incenter of triangle DZB. using these two facts you can easily get the correct answer.(after some very easy angle chase).

0 Helpful 0 Interesting 0 Brilliant 1 Confused

But angle CBE is already given to be 30 degrees.

Shashank Rammoorthy - 5 years, 6 months ago

Log in to reply

Sorry, i have corrected the solution now.

Reetun Maiti - 5 years, 6 months ago

Could you illustrate ?

Raven Herd - 5 years, 6 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...