We teach math and science to all students in the Bay Area

Our address is 621 Tully Road #215, San Jose, CA 95111

(408) 607-9314 / Stevevdinh@yahoo.com

Our Facebook website http://www.Facebook.com/MathUniversity

The areas of mathematics we teach cover

* Abstract algebra

* Algebra

* Algorithm

* Analytic Geometry

* Calculus

* Combinatorics

* Complex Analysis

* Differential Calculus

* Differential Equations

* Differential Geometry

* Discrete Math

* Elementary Algebra

* Functional Analysis

* Geometry

* Graph Theory

* Integral Calculus

* Linear Algebra

* Logic

* Mathematical Analysis

* Matrix Analysis

* Number Theory

* Numerical Analysis

* Pre-Algebra

* Pre-Calculus

* Quantitative Methods

* Real Analysis

* Set Theory

* Statistics and Probabbility

* Tensor Analysis

* Theory of Optimization

* Topology

* Trigonometry

* Vector Calculus

Math problems invented on 10/23/2012

1. Given a fixed point P inside a circle with center O. Two perpendicular chords AB and CD intersect at P (points A, B, C and D are on the circle). E is the symmetric point of P with respect to AC while F is the symmetric point of P with respect to BD. Prove that OE = OD.

2. Given a fixed point P inside a circle with center O and two perpen-dicular chords AB and CD intersecting at P (points A, B, C and D are on the circle). E is the symmetric point of P with respect to AC, and AE cuts the circle at J. Prove that EJ = BP.

Math problem invented on 10/03/2012

Given a point P inside triangle ABC with D, E and F be the feet of P onto BC, AC and AB, respectively. Prove that the circumradius of triangle DEF is not less than the inradius of triangle ABC.

Math problems invented on 09/10/2012

Math problems invented on 09/10/2012:

61. Given a ruler and a calculator just to be used to find the sine values of angles, show how to divide an angle into five equal smaller ones.

62. Let the bisectors of the exterior and interior angles of point A of triangle ABC intersect side BC at D and E, respectively. The circumcircle of triangle ADM where M is the midpoint of BC intersects AB and AC at I and J, respectively. IJ intersects BC at K; P and N are the midpoints of EK and IJ, respectively. Prove that E is also the incenter of triangle AHM.

63. Given a triangle ABC with circumcircle C and circumcenter O, AB > AC > BC and ∠BAC = 30°. Let D be a point on the minor arc BC of the circumcircle, E and F be points on AD such that AB⊥OE and AC⊥OF. The segments BE and CF intersect at P. Prove that OPis the bisector of ∠EPF.

64. Given a triangle ABC with circumcircle C and circumcenter O, AB > AC > BC and ∠BAC = 30°. Let D be a point on the minor arc BC of the circumcircle, E and F be points on AD such that AB⊥OE and AC⊥OF. The segments BE and CF intersect at P. Let K be a point on BP such that PK = CK. Prove that BK = OP.

65. Given a triangle ABC with circumcircle C and circumcenter O, AB > AC > BC and ∠BAC = 30°. Let D be a point on the minor arc BC of the circumcircle, E and F be points on AD such that AB⊥OE and AC⊥OF. The segments BE and CF intersect at P. Draw circle C1 with center P and radius CP to meet C at L. Prove that B, P and L are collinear.

Problem invented on 09/24/2012

Problem invented on 09/24/2012

ABC is a triangle in the plane. Let P be a point inside ABC. Prove that 3(PA² + PB² + PC²) ≥ AB² + BC² + CA². Find the condition for equality to occur.

Math problems invented on 09/09/2012

Math problems invented on 09/09/2012:

50. Find all triples of integers satisfying = and  +  = 2013.

51. In an acute triangle ABC points D, E, F are the feet of the altitudes from A, B and C, respectively. A line through D parallel to EF meets AC at Q and AB at R. Lines BC and EF intersect at P. Prove that the circumcircle of triangle PQR passes through the midpoint of BC. Prove that

, and ∠PIB = ∠DIP, ∠PJB = ∠DJP.

52. Let P be a point on the circumscribed circle of ΔABC and H be the orthocenter of ΔABC. Also let D, E and F be the points of intersection of the perpendicular from P to BC, CA and AB, respectively. N = C ∩ BH, Q = C ∩ CH, I = C ∩ PF, J = QC ∩ DF, S = BN ∩ PF, K = BN ∩ AC, T = PE ∩ QC. It is known that the three points D, E and F are collinear. Prove that the line DEF passes through the midpoint of the line segment ST.

53. The sum  + +  + … +  divisible by ? Find all possible values for .

54. and  are both nine-digit numbers from  to  and . Find  and  such that  –  = .

55. Let ABC be an arbitrary obtuse triangle. Prove that
DG + DH = R + r + DF, where r and R are the inradius and circumradius of triangle ABC, respectively, D the circumcenter of triangle ABC, DF, DG and DH the altitudes to the sides AC, AB and BC, respectively.

56. Points X, Y, Z are marked on the sides AB, BC, CD of the rhombus ABCD, respectively, so that XY || AZ. Let I be the inter-section of AY and XZ. Find the locus of point I.

57. For an acute triangle ABC, let H be the foot of the perpendicular from A to BC. Let M, N be the feet of the perpendicular from H to AB, AC, respectively. Define lA to be the line through A perpendicular to MN and similarly define lB and lC. Show that lA, lB and lC pass through a common point O.

Math problems invented on 09/08/2012

Math problems invented on 09/08/2012:

40. Given a triangle ABC with circumcircle C and circumcenter O, AB > AC > BC and ∠BAC = 30°. Let D be a point on the minor arc BC of the circumcircle, E and F be points on AD such that AB⊥OE and AC⊥OF. The segments BE and CF intersect at P. Prove that OP is the bisector of ∠EPF.

41. Given a triangle ABC with circumcircle C and circumcenter O, AB > AC > BC and ∠BAC = 30°. Let D be a point on the minor arc BC of the circumcircle, E and F be points on AD such that AB⊥OE and AC⊥OF. The segments BE and CF intersect at P. Let K be a point on BP such that PK = CK. Prove that BK = OP.

42. Given a triangle ABC with circumcircle C and circumcenter O, AB > AC > BC and ∠BAC = 30°. Let D be a point on the minor arc BC of the circumcircle, E and F be points on AD such that AB⊥OE and AC⊥OF. The segments BE and CF intersect at P. Draw circle C1 with center P and radius CP to meet C at L. Prove that the three points B, P and L are collinear.