In a circle with center O, a perpendicular is dropped from the center to a chord AB. Find the length of AO, if length of AB = 8 cm and CO = 3 cm.

2 cm

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3.5 cm

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5 cm

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6 cm

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Solution

The correct option is C 5 cm
The perpendicular from the centre of a circle to a chord bisects the chord.
$∴ A C = B C = 4 c m$
Given, CO = 3 cm.
Using Pythogoras theorem in $Δ A C O$ ,
we get, $(A O)^{2} = (C O)^{2} + (A C)^{2}$
$\Rightarrow (A O)^{2} = 3^{2} + 4^{2}$
$\Rightarrow (A O)^{2} = 25$
$\Rightarrow A O = 5 c m$ .

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In a circle with center O, a perpendicular is dropped from the center to a chord AB. Find the length of AO, if length of AB = 8 cm and CO = 3 cm.

The correct option is C 5 cmThe perpendicular from the centre of a circle to a chord bisects the chord. ∴AC=BC=4 cm Given, CO = 3 cm. Using Pythogoras theorem in ΔACO, we get, (AO)2=(CO)2+(AC)2 ⇒(AO)2=32+42 ⇒(AO)2=25 ⇒AO=5 cm.