Problem B. 4135. (December 2008)

B. 4135. M is a point in the interior of a square ABCD, such that DCM $\angle$ =MAC $\angle$ =25^o. Find the measure of the angle ABM.

(4 pont)

Deadline expired on January 15, 2009.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás: Nyilván $ACM\sphericalangle=45^\circ-DCM\sphericalangle=20^\circ$ , és így $AMC\sphericalangle=135^{\circ}$ . A B középpontú, AB sugarú körnek az MB szakasz B-n túli meghosszabbításával vett metszéspontja legyen N. A kerületi és középponti szögek tételét alkalmazva kapjuk, hogy $ANC\sphericalangle=ABC\sphericalangle/2=45^\circ$ , vagyis az ANCM négyszög húrnégyszög és

$ABM\sphericalangle=2ANM\sphericalangle=2ACM\sphericalangle=40^\circ.$

Statistics:

132 students sent a solution.

4 points: 91 students.

3 points: 9 students.

2 points: 11 students.

1 point: 6 students.

0 point: 3 students.

Unfair, not evaluated: 12 solutionss.

Problems in Mathematics of KöMaL, December 2008

132 students sent a solution.
4 points:	91 students.
3 points:	9 students.
2 points:	11 students.
1 point:	6 students.
0 point:	3 students.
Unfair, not evaluated:	12 solutionss.

Already signed up?
New to KöMaL?