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Find the length of the chord AC where AB and CD are the two diameters perpendicular to each other of a circle with radius `4sqrt(2)` cm and also find ∠OAC and ∠OCA

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#### Solution

Radius of a circle = `4sqrt(2)` cm

In the right ΔAOC,

AC^{2} = OA^{2} + OC^{2}

AC^{2} = `(4sqrt(2))^2 + (4sqrt(2))^2`

= 32 + 32 = 64

AC = `sqrt(64)`

= 8

Length of the chord = 8 cm,

∠OAC = ∠OCA = 45°

Since OAC is an isosceles right angle triangle.

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