MathDB

1

Part of 2003 National High School Mathematics League

Problems(2)

Delete the Profect Squares

Source: 2003 National High School Mathematics League, Exam One, Problem 1

3/16/2020
Delete all perfect squares in 1,2,3,⋯1,2,3,\cdots, then the 2003rd number is (A)2046(B)2047(C)2048(D)2049\text{(A)}2046\qquad\text{(B)}2047\qquad\text{(C)}2048\qquad\text{(D)}2049
Geometry

Source: 2003 National High School Mathematics League, Exam Two, Problem 1

3/16/2020
Draw two tangents to the circle from point PP outside a circle, touching the circle at AA and BB, then draw a secant line passes PP, intersecting the circle at points CC and DD (CC is between PP and DD). QQ is a point on the chord CDCD such that ∠DAQ=∠PBC\angle DAQ=\angle PBC. Prove that ∠DBQ=∠PAC\angle DBQ=\angle PAC.
geometry