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From an external point A, two tangents AB and AC have been drawnto a circle touching the circle at B and C respectively. P and
Q are points on AB and AC respectively such that PQ touchesthe circle at R. IfAB = 11 cm, AP=7 cm and AQ = 9 cm, then find
the length of PQ (in cm).
7
5
8
6
- The tangents from a common external point are equal, so AB = AC = 11 cm.
- Since AP and AQ are parts of AB and AC, respectively: AP = 7 cm and AQ = 9 cm.
- Therefore, BP = AB - AP = 11 - 7 = 4 cm and CQ = AC - AQ = 11 - 9 = 2 cm.
- Since PQ is another tangent, and the tangents from an external point to a circle are equal in length to parts of those tangents, we can conclude:
- By the tangent-segment theorem or power of a point: AP * AQ = BP * CQ + PR^2 or simply PQ = BP + CQ when tangential from one external segment to another.
- So, PQ = 4 cm + 2 cm = 6 cm.
- Thus, the length of PQ is 6 cm.
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