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

The values of tan ∠RQT, tan ∠SQT and tan ∠PQT form a geometric sequence, and:
The values of cot ∠SQT, cot ∠RQT and cot ∠SQR form an arithmetic sequence.

Determine the area of the triangle PQR.