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 = 24 cm and OD = 5 cm, then find the circumradius.

10 cm

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11 cm

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12 cm

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13 cm

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Solution

The correct option is D
13 cm

Given AB = AC, OD $⊥$ BC, BC = 24 cm and OD = 5 cm

We know that that perpendicular from the centre bisects the chord. Also given BC = 24 cm.

So, BD = 12 cm

Join AB.

Now, $(O B)^{2} = (B D)^{2} + (O D)^{2} = 12^{2} + 5^{2} = 144 + 25 = 169$

$∴ O B = circumradius = 13$ cm

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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 = 24 cm and OD = 5 cm, then find the circumradius.

The correct option is D 13 cm Given AB = AC, OD ⊥ BC, BC = 24 cm and OD = 5 cm We know that that perpendicular from the centre bisects the chord. Also given BC = 24 cm. So, BD = 12 cm Join AB. Now, (OB)2=(BD)2+(OD)2=122+52=144+25=169 ∴OB=circumradius=13 cm