Question

two chords pq and pr of a circle are equal. prove that the centre of the circle lies on the angle bisector of <qpr

Answer 1

Answer:

Step-by-step explanation:

Hi,

Given PQ and PR are equal chords of the circle.

Let the center of the circle be 'O'

Let us join P and O,

Consider triangles ΔPOQ and ΔPOR,

OP =OP = radius of the circle(common side)

OQ = OR = radius of the circle

PQ = PR ( equal chords)

Hence both the triangles, Δ POQ ≅ Δ POR ,

hence ∠QPO = ∠RPO

Thus, PO is the angular bisector of angle P.

Hence , center of the circle lies on the angular bisector .

Hope, it helped !