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CMI Entrance 2019 Problem from Transformation Geometry

Let's discuss a problem from CMI Entrance Exam 2019 based on the Inscribed Angle Theorem or Central Angle Theorem and Transformation Geometry.

The Problem:

Let $A B C D$ be a parallelogram. Let 'O' be a point in its interior such that $\angle A D B+\angle D O C=180^{\circ}$. Show that $\angle O D C=\angle O B C$.

The Solution:

Some useful resources:

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