In figure ,PA and PB are tangent to a circle with centre O drawn from an external point P. QR is tangent at point S. prove that PQ + QS = PR + RS

PA = PB (tangents from common exterior point to a circle are equal)
=> PQ + AQ = PR + BR
But, AQ = QS (tangents from common exterior point to a circle are equal)
and, BR = RS (tangents from common exterior point to a circle are equal)
Therefore, PQ + QS = PR + RS
Hence, proved.