In triangle PQT, R is on side PT such that QR=QP. Also, QS is an altitude, and QT=10. The values of tan RQT, tan SQT, and tan PQT form a geometric progression, and the values of cot SQT, cot RQT, and cot SQR form an arithmetic progression. Find the area of triangle PQR.
In triangle PQTR is on side PT such that QR=QP. Also, QS is an altitude, and QT=10. The values of tan RQT, tan SQT, and tan PQT form a geometric progression, and the values of cot SQT, cot RQT, and cot SQR form an arithmetic progression. Find the area of triangle PQR.