Question

Construct a $\angle$ABC = 30${}^{\circ }$. Mark a point D on BC such that BD = 5 cm. Find the radius of the circle to touch AB at B and also pass through D.

• A. 5.5 cm
• B. 2.5 cm
• C. 3.464 cm
• D. 6.4 cm

Answer 1

The correct option is C

3.464 cm

$\angle$ABC = 30${}^{\circ }$ is drawn.

BE is drawn perpendicular to AB at B.

BD = 5 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.

Consider triangle OBD



$cos\left({60}^{\circ }\right)=\frac{BN}{OB}$

$⟹\frac{1}{2}=\frac{2.5}{OB}$

$⟹OB=5$