Find the length of AC in cm - if the radius of the circle is 4 cm-A- 4 cmB- 6 cm-C- 2-2 -3 cm D- 4-4 -2 cm

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Standard IX

Mathematics

Diameter Subtends Right Angle at the Circumference

Find the leng...

Question

Find the length of AC (in cm), if the radius of the circle is 4 cm.

4 cm

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6 cm

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$(2 + 2 \sqrt{3} c m)$

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$(4 + 4 \sqrt{2} c m)$

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Solution

The correct option is D
$(4 + 4 \sqrt{2} c m)$

Join the points B and O

In $Δ A O B, A B = O B = 4 c m$ [Isosceles right angled triangle]

$A O = 4 \sqrt{2} c m$ (Using Pythagoras Theorem)

So, AC = AO + OC $= 4 + 4 \sqrt{2} c m$

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Find the length of AC (in cm), if the radius of the circle is 4 cm.

The correct option is D (4+4√2 cm) Join the points B and O In ΔAOB,AB=OB=4 cm [Isosceles right angled triangle] AO=4√2 cm (Using Pythagoras Theorem) So, AC = AO + OC =4+4√2 cm

The correct option is D
$(4 + 4 \sqrt{2} c m)$

Join the points B and O

In $Δ A O B, A B = O B = 4 c m$ [Isosceles right angled triangle]

$A O = 4 \sqrt{2} c m$ (Using Pythagoras Theorem)

So, AC = AO + OC $= 4 + 4 \sqrt{2} c m$