Question

Activity II : In the adjoining figure seg QR is a chord of the circle with centre 0. P is the midpoint of the chord QR. If QR = 24, OP = 10, find radius of the circle. to find solution of the problem, write the theorems that are useful.
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Answer 1

Answer:

The segment joining the centre of a circle and the midpoint of a chord is perpendicular to the chord. ii. In a right angled triangle, sum of the squares of the perpendicular sides is equal to square of its hypotenuse. QP = 1/2 (QR) [P is the midpoint of chord QR] 1/2 x 24 = 12 units Also, seg OP ⊥ chord QR [The segment joining centre of a circle and midpoint of a chord is perpendicular to the chord] In ∆OPQ, ∠OPQ = 90° ∴ OQ2 = OP2 + QP2 [Pythagoras theorem] = 102 + 122 = 100 + 144 = 244 ∴ OQ = √244 = 2√61 units. ∴ The radius of the circle is 2√61 units.Read more on Sarthaks.com - https://www.sarthaks.com/851299/the-adjoining-figure-seg-chord-the-circle-with-centre-the-midpoint-the-chord-find-radius-the

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