Question

In the given figure if $\angle$ BAC = ${60}^{\circ }$, then which of the following statements are true?

• A. AB = AC
• B. AB = BC
• C. BC = AC
• D. AB > AC

Answer 1

Answer: (A), (B), (C)

BC = AC

For constructing an angle of 60${}^{\circ }$, we draw an arc of arbitrary radius from one of the end points 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 end point gives a 60${}^{\circ }$ angle. Since B and C are on arcs of same radii centred at A, AB = AC. Also, B is on arc centred at C having the same radius, so, BC = AC. So, AB = BC = AC.