MathDB

1

Part of 1998 National High School Mathematics League

Problems(2)

Logarithm

Source: 1998 National High School Mathematics League, Exam One, Problem 1

3/8/2020
If a>1,b>1,lg⁡(a+b)=lg⁡a+lg⁡ba>1,b>1,\lg(a+b)=\lg a+\lg b, then the value of lg⁡(a−1)+lg⁡(b−1)\lg(a-1)+\lg(b-1) is (A)lg⁡2(B)1(C)0(D)\text{(A)}\lg2\qquad\text{(B)}1\qquad\text{(C)}0\qquad\text{(D)} not sure
logarithms
Geometry

Source: 1998 National High School Mathematics League, Exam Two, Problem 1

3/9/2020
Circumcenter and incentre of △ABC\triangle ABC are O,IO,I. ADAD is the height on side BCBC. If II is on line OCOC, prove that the radius of circumcircle and escribed circle (in \angle BAC) are equal.
geometrycircumcircleincenter