MathDB

10

Part of 2003 AIME Problems

Problems(2)

Isosceles triangle

Source:

5/11/2006
Triangle ABCABC is isosceles with AC=BCAC = BC and ∠ACB=106∘\angle ACB = 106^\circ. Point MM is in the interior of the triangle so that ∠MAC=7∘\angle MAC = 7^\circ and ∠MCA=23∘\angle MCA = 23^\circ. Find the number of degrees in ∠CMB\angle CMB.
trigonometryAMCAIMEgeometrytrig identitiesLaw of SinesLaw of Cosines
Optimizing a Sum

Source:

12/26/2006
Two positive integers differ by 60.60. The sum of their square roots is the square root of an integer that is not a perfect square. What is the maximum possible sum of the two integers?
quadraticssymmetryalgebra