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. Prove that the centre of the park lies on the angle bisector of angle
BAC . Which mathematical concept is used in the above problem?​

Answer 1

Answer:

hello

Step-by-step explanation:

Given : A circle COr ^ h , and chord AB = chord AC

. AD is bisector of +CAB .

To prove : Centre O lies on the bisector of +BAC .

Construction: Join BC , meeting bisector AD of

+BAC , at M .

Proof : In triangles BAM and CAM ,

AB = AC (given)

+BAM = +CAM (given)

and AM = AM (common)

TBAM , TCAM (SAS)

BM = CM

and +BMA = +CMA

As + + BMA CMA + = 180c (linear pair)

+BMA = +CMA = 90c

AM is the perpendicular bisector of the chord BC .

AM passes through the centre O.

[Perpendicular bisector of chord of a circle passes

through the centre of the circle]

Hence, the centre of the park lies on the angle bisector

of +BAC

HOPE THIS HELP