Question

Find the length of the chord AC where AB and CD are the two diameters perpendicular to each other of a circle with radius 42cm and also find ∠OAC and ∠OCA

Answer 1

i have attached answer for you
both the angle will be equal to 45 degree....

Answer 2

AC = 42√2 cm , ∠OAC = ∠OCA = 45°  where AB and CD are the two diameters perpendicular to each other of a circle with radius 42cm

Step-by-step explanation:

AB & CD are two Diameter perpendicular to each other of a circle with radius 42cm

AB & CD intersect at O

=> OA = OB = OC = OD = Radius = 42 cm

in Δ OAC

OA = OC

=> ∠OAC = ∠OCA

∠AOC = 90° ( as Diameters are perpendicular to each other)

∠OAC +  ∠OCA + ∠AOC = 180°

=> ∠OAC +  ∠OCA + 90° = 180°

=> ∠OAC +  ∠OCA = 90°

∠OAC = ∠OCA

=> ∠OAC = ∠OCA = 45°

AC² = OA² + OC²

=> AC² = 42² + 42²

=> AC = 42√2 cm

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