MathDB

2

Part of 1994 Turkey Team Selection Test

Problems(2)

Turkey TST 1994 - P2

Source:

3/13/2011
Let OO be the center and [AB][AB] be the diameter of a semicircle. EE is a point between OO and BB. The perpendicular to [AB][AB] at EE meets the semicircle at DD. A circle which is internally tangent to the arc \overarc{BD} is also tangent to [DE][DE] and [EB][EB] at KK and CC, respectively. Prove that EDC^=BDC^\widehat{EDC}=\widehat{BDC}.
geometry proposedgeometry
Turkey TST 1994 - P5

Source:

3/13/2011
Show that positive integers ni,min_i,m_i (i=1,2,3,⋯ )(i=1,2,3, \cdots ) can be found such that lim⁡i→∞2ni3mi=1 \mathop{\lim }\limits_{i \to \infty } \frac{2^{n_i}}{3^{m_i }} = 1
limitlogarithmsalgebra proposedalgebra