The length of a chord PQ of a circle with its centre O is 4cm. and the distance of PQ. the point o is 2.1 cm . Let us write by calculating, the length of diameter.
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Step-by-step explanation:
Length of cord PQ=4cm.
let the line passing through O intersect PQ at R
such that R is perpendicular bisector of PQ.
so, PR=QR=2cm.
Length of OR=2.1cm
OQ=OP=r (radius of circle)
Consider ∆POR, in which angleR=90°.(by construction)
Using Pythagorean triplet:
OP²=OR²+PR².
=>r²=(2.1)²+2²
=r²=4.41+4
=>r=√8.41=2.9cm.
D=2r=2×2.9=5.8
Diameter of the circle=5.8cm.
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