MathDB

1

Part of 2002 National High School Mathematics League

Problems(2)

A Function

Source: 2002 National High School Mathematics League, Exam One, Problem 1

3/12/2020
The increasing interval of f(x)=log⁡12(x2−2x−3)f(x)=\log_{\frac{1}{2}}(x^2-2x-3) is (A)(−∞,−1)(B)(−∞,1)(C)(1,+∞)(D)(3,+∞)\text{(A)}(-\infty,-1)\qquad\text{(B)}(-\infty,1)\qquad\text{(C)}(1,+\infty)\qquad\text{(D)}(3,+\infty)
function
Geometry

Source: 2002 National High School Mathematics League, Exam Two, Problem 1

3/16/2020
In △ABC\triangle ABC, ∠A=60∘\angle A = 60^{\circ}, AB>ACAB>AC, OO is the circumcenter and HH is the intersection point of two heights BEBE and CFCF. Points MM and NN lie on segments BHBH and HFHF respectively, and BM=CNBM=CN. Find the value of MH+NHOH\frac{MH+NH}{OH}.
geometry