Question

In the following figure, write BC, AC, and CD in ascending order of their lengths.

Answer 1

In ΔABC,

AB = AC

⇒ ∠ABC = ∠ACB  ..(angles opposite to equal sides are equal)

⇒ ∠ABC = ∠ACB = 67°

⇒ ∠BAC = 180° - ∠ABC - ∠ACB   ...(Angle sum property)

⇒ ∠BAC = 180° - 67° - 67° = 46°

Since ∠BAC < ∠ABC, we have

BC < AC                              ...(1)

Now, ∠ACD = 180° - ACB  ...(Linear pair)

⇒ ∠ACD = 180° - 67° = 113°

Thus, in ΔACD,

∠CAD = 180°- ∠ACD - ∠ADC

⇒ ∠CAD = 180° - 113° - 33° = 34°

Since ∠ADC <  ∠CAD, we have

AC < CD                            ...(2)

From (1) and (2), we have

BC < AC < CD.