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.

(In reply to Where is S? by Harry)

Just saw the comment.

INDEED, the altitude is QS instead of RS as mentioned in the problem.

This is a typographical anomaly which is regretted.

Posted by K Sengupta on 2014-08-17 02:01:55