Question

In the given figure if $\angle$ABC = ${60}^{\circ }$, AB = AC, then

• A. AB=AC
• B. AB=BC
• C. BC = AC
• D. none of the above

Answer 1

Answer: (B), (C)

The correct options are
B

AB=BC

C

BC = AC

For constructing an angle of 60${}^{\circ }$, we draw an arc of arbitrary radius from one of the endpoints cutting the base of the angle. From this intercept, we draw another arc of the same radius cutting the previous arc. Joining the intercept of arcs to the endpoint gives a 60${}^{\circ }$ angle. Since B and C are on arcs of same radii centred at A, AB = AC. Also, B is on the arc centred at C having the same radius, so, BC = AC. So, AB = BC = AC.