Prove that the points (0, −5), (4, 3) and (−4, −3) lie on the circle centered at the origin with radius 5.

Formula used:

Let the point A (0, –5), B (4, 3) and C (–4, –3) lie on the circle with center O (0, 0)

Distance of AO

⇒ AO = √ ((0 – 0)² + (0 – (–5))²)

⇒ AO = √ ((0 – 0)² + (0 + 5)²)

⇒ AO = √ ((0)² + (5)²)

⇒ AO = √ (0 + 25)

⇒ AO = √ 25

⇒ AO = 5

Distance of BO

⇒ BO = √ ((0 – 4)² + (0 – 3)²)

⇒ BO = √ ((–4)² + (–3)²)

⇒ BO = √ (16 + 9)

⇒ BO = √ 25

⇒ BO = 5

Distance of CO

⇒ CO = √ ((0 – (–4))² + (0 – (–3))²)

⇒ CO = √ ((0 + 4)² + (0 + 3)²)

⇒ CO = √ ((4)² + (3)²)

⇒ CO = √ (16 + 9)

⇒ CO = √ 25

⇒ CO = 5

∴ AO = BO = CO = 5 = Radius

Hence, point A, B and C lie on the circle.