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In the adjoining figure, seg PS is the median of APQR and PT ⊥ QR. Prove that,

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i. QS = SR = 1/2 QR (i) [S is the midpoint of side QR]

∴ In ∆PSR, ∠PSR is an obtuse angle [Given] and PT ⊥ SR [Given, Q-S-R]

∴ PR2 = SR2 + PS2 + 2 SR × ST (ii) 

[Application of Pythagoras theorem]

PT ⊥QS [Given, Q-S-R]

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