A geometry problem by Danish Ahmed

Geometry Level 3

In triangle \(PQR\), \(PQ = QR\) and \(RS\) is the altitude. \(PR\) is extended to point \(T\) such that \(QT = 10\).

The values of \(\tan \angle RQT, \tan \angle SQT\) and \(\tan \angle PQT\) form a geometric sequence, and:

The values of \(\cot \angle SQT, \cot \angle RQT\) and \(\cot \angle SQR\) form an arithmetic sequence.

If the area of the triangle \(PQR\) can be exprssed as \(\dfrac{a}{b}\) where \(gcd(a ,b) = 1\) .

Then \(a + b =\)


Problem Loading...

Note Loading...

Set Loading...