Question

Choose the correct word that completes each statement about inscribing a square in a circle.

The second diameter that is constructed or copied is_________ to the first diameter.
parallel
perpendicular

The chord that connects the endpoints of the diameters forms a(n) __________ triangle.
equilateral
scalene
isosceles The side of the inscribed square has a length ________ equal to the radius, r.
sometimes
always
never

Answer 1

1. Perpendicular

2. Isosceles

3. Never

Explanation:

Answer 2

1. Perpendicular

2. Isosceles

3. Never

Explanation:

1. AC ⊥ BD because diameter of a square are perpendicular bisector of each other.

2. In Δ AOB , By using pythagoras : AB² = OA² + OB² .......( 1 )

In Δ COB , By using pythagoras : BC² = OC² + OB² ..........( 2 )

But, OA = OC because both are radius of same circle

So, by using equations ( 1 ) and ( 2 ), We get AB = BC ≠ AC

⇒ ABC is a triangle having two equal sides so ABC is an isosceles triangle.

3. The side can never be equal to radius of circle because the side of the square will be chord for the circle and in a circle chord can never be equal to its radius