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Question
In the given figure, ∠Q = 90°, PS is a median om QR from P, and RT divides PQ in the ratio 1 : 2. Find: `("tan" ∠"TSQ")/("tan"∠"PRQ")`
Solution
As PS is the median on QR from P.
∴ QS = SR
⇒ QR = 2QS
and RT divides PQ in the ratio 1 : 2
∴ QT = x and PT = 2x
⇒ PQ = 3x
`("tan" ∠"TSQ")/("tan"∠"PRQ")`
= `("QT"/"QS")/("PQ"/"QR")`
= `"QT"/"QS" xx "QR"/"PQ"`
= `x/"QS" xx (2"QS")/(3x)`
= `(2)/(3)`.
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