Math Problem Statement

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Solution

The image you uploaded contains two geometry problems written in Vietnamese. Here's a brief translation of the tasks:

B1: For triangle ΔABC\Delta ABC, where AB=ACAB = AC:

  • Let MM be on segment ACAC and NN on segment ABAB, with the conditions AM=ANAM = AN.
  • Prove the following:
    • (a) ABM=ACN\triangle ABM = \triangle ACN
    • (b) Point II is where the perpendiculars from BMBM and CNCN meet.
    • (c) INB=INC\triangle INB = \triangle INC
    • (d) Prove that line MNBCMN \parallel BC.

B2: For the circle xOyxOy, with points CC, DxOyD \in xOy, such that OA=OCOA = OC and AB=CDAB = CD:

  • Prove the following:
    • (a) OAD=OBC\triangle OAD = \triangle OBC
    • (b) Let MM be the intersection of BCBC and ADAD, proving AMB=MDC\triangle AMB = \triangle MDC
    • (c) Prove that OMOM is perpendicular to line xx.
    • (d) Prove that OMOM is perpendicular to ACAC.
    • (e) Prove that ACBDAC \parallel BD.

If you need help with solving any part of these problems, let me know which one you'd like to work on first!

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Circle Theorems
Parallel Lines
Congruent Triangles
Perpendiculars

Formulas

Congruence criteria for triangles
Properties of parallel lines
Perpendicular bisector theorem

Theorems

Isosceles triangle theorem
Angle Bisector Theorem
Perpendicular from a point to a line

Suitable Grade Level

Grades 9-12