In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.

4 cm

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5 cm

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8 cm

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10 cm

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Solution

The correct option is B
5 cm

Given AB = AC, OD $⊥$ BC, BC = 8 cm and OD = 3 cm

We know that that perpendicular from the centre bisects the chord. Also given BC = 8 cm.

So, BD = 4 cm

Join OB.

Now, $(O B)^{2} = (B D)^{2} + (O D)^{2} = 4^{2} + 3^{2} = 16 + 9 = 25$

$∴ O B = circumradius = 5$ cm

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Similar questions

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(c) 8 cm
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∠

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^{\circ}

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O D

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In the figure, O is the circumcentre of the triangle ABC, AB = AC and the line OD is perpendicular to the side BC. If BC = 8 cm and OD = 3 cm, then find the circumradius.

The correct option is B 5 cm Given AB = AC, OD ⊥ BC, BC = 8 cm and OD = 3 cm We know that that perpendicular from the centre bisects the chord. Also given BC = 8 cm. So, BD = 4 cm Join OB. Now, (OB)2=(BD)2+(OD)2=42+32=16+9=25 ∴OB=circumradius=5 cm