Construct a $∠$ ABC = 30 $^{\circ}$ . Mark a point D on BC such that BD = 6 cm. Find the radius of the circle to touch the line AB at B and also pass through D.

5.5 cm

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2.5 cm

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3.464 cm

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6.4 cm

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Solution

The correct option is C
3.464 cm

$∠$ ABC = 30 $^{\circ}$ is drawn.

BE is drawn perpendicular to AB at B.

BD = 6 cm is taken from BC.

Perpendicular bisector of BD is drawn which intersects BE at O.

Taking O as centre and OB as radius a circle is drawn which pass through B and D.

In triangle BOD

OB = OD

Therefore, $∠ O B D = ∠ O D B = 60^{\circ}$

So, $∠ B O D = 180^{\circ} - ∠ O B D - ∠ O D B$

$∠ B O D = 60^{\circ}$

All three angles of triangle BOD are equal. So it is a equilateral triangle.

Therefore, OB = OB = BD = 6cm

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