Question

Roja, Renu and Reena are three friends. They decided to sweep a circular park near their homes. They divided the park into three parts by two equal chords AB and AC for convenience. [3](i) Prove that the centre of the park lies on the angle bisector of +BAC .(ii) Which mathematical concept is used in the above problem?​

Answer 1

The centre of prak lies on the angle bisector as AO is the angle bisector by CPCT.

As equal chords are subtended equal angle at center, thus -

Therefore,

∠AOB=∠AOC  --- eq 1

In ΔAOB  and ΔAOC,

∠AOB=∠AOC ( From equation 1 )      

AO=AO  (Common side)      

OB=OC  ( Radius of the circle)

Therefore, △AOB≅△AOC  by SAS congruency

Then ∠OAB =∠OAC ( By CPCT)

Hence, AO is the angle bisector of ∠BAC