A geometry problem by Akshay Yadav

Geometry Level 5

The figure represents above shows a Cartesian plane.

In the given figure \(O= (0,0)\) is the center of a circle with radius \(\dfrac{5}{2}\) units. \(\angle ABC =18^\circ\) and \(\angle ADC = 9^\circ\).

If the \(x\)-coordinates of \(D\) are in form


Note that \(a\), \(b\) and \(c\) are mutually prime positive integers.

Find \(a+b+c\) .

You may use the fact that \(\sin 18^\circ=\dfrac{\sqrt{5}-1}{4}\).

Clarification: Angles are measured in degrees.

It is a challenge for all those who love geometry! This is the toughest problem that I have posted on Brilliant till now.

Problem Loading...

Note Loading...

Set Loading...