In figure 3.80, if PQ = 6, QR = 10, PS = 8 find TS.

Figure: From the external point P two secants are drawn: P–Q–R and P–S–T.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: TS = 4

PR = PQ + QR = 6 + 10 = 16. By the theorem of secants intersecting outside a circle,

\[PS \times PT = PQ \times PR\] \[8 \times PT = 6 \times 16 = 96\] \[PT = 12\] \[TS = PT - PS = 12 - 8 = 4\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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