The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle. In the below figure $ \mathrm{AB} $ is a diameter of the circle; $ \mathrm{C} $ is its centre. Express the diameter of the circle $ (d) $ in terms of its radius $ (r) $.
"
Given:
The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle.
In the given figure \( \mathrm{AB} \) is a diameter of the circle; \( \mathrm{C} \) is its centre.
To do:
We have to express the diameter of the circle \( (d) \) in terms of its radius \( (r) \).
Solution:
\( \mathrm{AB} \) is the diameter of the circle
From the figure,
$AB=AC+BC$
$=r+r$
$=2r$
$d=2r$
The diameter of the circle \( (d) \) in terms of its radius \( (r) \) is $d=2r$.
Related Articles
- Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.
- 1. Fill in the blanks:(i) The centre of a circle lies in ______ of the circle. (exterior/ interior)(ii) A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)(iii) The longest chord of a circle is a ________ of the circle.(iv) An arc is a ________ when its ends are the ends of a diameter.(v) Segment of a circle is the region between an arc and ________ of the circle.(vi) A circle divides the plane, on which it lies, in _________ parts.
- What is the Diameter of circle?
- The centre of a circle is $(2a, a – 7)$. Find the values of $a$ if the circle passes through the point $(11, -9)$ and has diameter $10\sqrt2$ units.
- Draw any circle and mark points \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) such that(a) \( \mathrm{A} \) is on the circle.(b) \( \mathrm{B} \) is in the interior of the circle.(c) \( \mathrm{C} \) is in the exterior of the circle.
- The centre of a circle is \( (2 a, a-7) \). Find the values of \( a \) if the circle passes through the point \( (11,-9) \) and has diameter \( 10 \sqrt{2} \) units.
- (a) Is every diameter of a circle also a chord?(b) Is every chord of a circle also a diameter?
- Find the diameter of the circle if radius is 6.2 cm.
- Ratio of the circumference of a circle to its diameter is denoted by the symbol____.
- Fill in the blanks:A point whose distance from the centre of a circle is greater than its radius lies in …….. of the circle.
- In a circle of radius \( 6 \mathrm{~cm} \), a chord of length \( 10 \mathrm{~cm} \) makes an angle of \( 110^{\circ} \) at the centre of the circle. Find the circumference of the circle.
- In a circle of radius \( 6 \mathrm{~cm} \), a chord of length \( 10 \mathrm{~cm} \) makes an angle of \( 110^{\circ} \) at the centre of the circle. Find the area of the circle.
- Write True or False: Give reasons for your answers.(i) Line segment joining the centre to any point on the circle is a radius of the circle.(ii) A circle has only finite number of equal chords.(iii) If a circle is divided into three equal arcs, each is a major arc.(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.(v) Sector is the region between the chord and its corresponding arc.(vi) A circle is a plane figure.
- The centre of a circle is $( -6,\ 4)$. If one end of the diameter of the circle is at $( -12,\ 8)$, then find the point of the other end.
- Draw a circle with centre at point $O$ and radius $5\ cm$. Draw its chord $AB$, draw the perpendicular bisector of line segment $AB$. Does it pass through the centre of the circle?
Kickstart Your Career
Get certified by completing the course
Get Started