From an external point A, two tangents AB and AC have been drawn to a circle touching the circle at B and C respectively. P and Q are points on AB and AC respectively such that PQ touches the circle at R. If AB = 11 cm, AP = 7 cm and AQ = 9 cm, then find the length of PQ (in cm).

By the property of tangents from an external point, AB = AC (both from point A). The tangent segments from point P to the circle are equal: PB = PR. Similarly, from point Q: QC = QR. Given AB = 11, AP = 7, we find PB = AB - AP = 4. Given AQ = 9, we find QC = AC - AQ = 11 - 9 = 2. For PQ = PR + RQ: PQ = PB + QC = 4 + 2 = 6 cm.