The points A(2, 3), B(3, 5), C(7, 7) and D(5, 6) are such that: -Maths 9th

The points A(2, 3), B(3, 5), C(7, 7) and D(5, 6) are such that: -Maths 9th
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Answer :

(d) 24 unitsAB ⊥ chord PQ ⇒ AB bisects chord PQ ⇒ PQ = 2PB. AB = \(\sqrt{(2-5)^2+(-3-1)^2}\) = \(\sqrt{(-3)^2+(-4)^2}\)= \(\sqrt{9+16}\) = \(\sqrt{25}\) = 5AP = radius of circle = 13 ∴ By Pythagoras’ Theorem, PB = \(\sqrt{AP^2-AB^2}\)= \(\sqrt{169-25}\) = \(\sqrt{144}\) = 12 units∴ PQ = 2 × PB = 24 units.
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