Circles | MCQs

Explanation

Given:

Radius (r) = 13 cm

Distance from center to chord (d) = 5 cm

Let's draw a perpendicular from the center to the chord. This will bisect the chord.

Using the Pythagorean theorem:

r² = d² + (half chord)²

13² = 5² + (half chord)²

169 = 25 + (half chord)²

(half chord)² = 169 - 25

= 144

half chord = √144

= 12 cm

Length of chord = 2 × half chord

= 2 × 12

= 24 cm

Explanation

A circle can have an infinite number of tangents.

Since a circle is defined as a set of points equidistant from a fixed point,

And each point on the circle can have a tangent line, there are infinitely many possible tangent lines. 

Explanation

Explanation

Let the circumference of the circle = perimeter of the square = P  

- Circumference of circle = 2πr  

- Perimeter of square = 4a (a = side of square)  

So, 2πr = 4a ⇒ a = (πr)/2

- Area of circle = πr²  

- Area of square = a² = (πr/2)² = (π²r²)/4

Now compare:

πr² (circle) vs. (π²r²)/4 (square)  

Divide both sides:  

(πr²) / ((π²r²)/4) = 4/π > 1 ⇒ area of circle > area of square.

Explanation

Circumference =2πr.

∴2πr=31.4.

2×3.14×r=31.4.

r=5cm.

Area =πr2.

Area =3.14×(25)2

=78.5cm2.

Explanation

The total angle around a circle is always 360 degrees.

This represents a full rotation or complete turn.

Explanation

A circum-circle is a circle that passes through all the vertices of a triangle.

Its center is called the circumcenter.

Explanation

A circle can have an infinite number of tangents.

Because a tangent can be drawn at any point on the circumference of the circle, each touching it at exactly one point.

Explanation

The area of a circle can be expressed in terms of its circumference C as:

A = C^2 / 4π

This is because the circumference C is related to the radius r by:

C = 2πr

And the area A is related to the radius r by:

A = πr^2

Substituting the expression for r in terms of C, we get:

A = C^2 / 4π

Explanation

A tangent line intersects a circle at 1 point.

This is because a tangent touches the circle at exactly one point without crossing it.