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 = 16 cm and OD = 6 cm, then find the circumradius.

5 cm

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8 cm

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10 cm

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15 cm

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Solution

The correct option is C
10 cm

Given AB = AC, OD $⊥$ BC, BC = 16 cm and OD = 6 cm

We know that that perpendicular from the centre bisects the chord. Also given BC = 16 cm.

So, BD = 8 cm

Join OB.

Now, $(O B)^{2} = (B D)^{2} + (O D)^{2} = 8^{2} + 6^{2} = 64 + 36 = 100$

$∴ O B = circumradius = 10$ 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 = 16 cm and OD = 6 cm, then find the circumradius.

The correct option is C 10 cm Given AB = AC, OD ⊥ BC, BC = 16 cm and OD = 6 cm We know that that perpendicular from the centre bisects the chord. Also given BC = 16 cm. So, BD = 8 cm Join OB. Now, (OB)2=(BD)2+(OD)2=82+62=64+36=100 ∴OB=circumradius=10 cm