Question

Find the diameter of the circle whose chord is 10cm and distance from centre to the chord is 12cm.

Answer 1

the line drawn from the centre to the chord bisects the chord
using pythagorus theorm find the radius
now double the radius
u ll get ur diametre

Answer 2

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{ \red{Required \;Question \;:}}}}}\\ \\\end{gathered}$

Find the diameter of the circle whose radius is 10cm and distance from centre to the chord is 12cm.

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{ \blue{detailed\;explanation\;:}}}}}\\ \\\end{gathered}$

In this question we need to find the diameter of the circle in which radius is of 10cm from the centre to the circle and chord is of 12 cm.

Now first we will going to find the half of chord and then by using Pythagoras theorem we will find the diameter of the circle.

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{Required\;solution\;:}}}}}\\ \\\end{gathered}$

Step 1 :

Let us suppose the centre of the circle as point C.

Step 2 :

Here , for finding diameter first we need to find the half of the chord.

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: l(ab) = \frac{1}{2} \times l(pb)\;}}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: l(ab) = \frac{1}{2} \times 12}}}}}\\ \\\end{gathered}$

Property : The perpendicular drawn from the centre of the circle to its chord bisects the chord.

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{l(pb) = 6cm}}}}}\\ \\\end{gathered}$

Hence , l(pb) = 6cm .

________________

Now for finding the diameter :

In right angled triangle , by using Phythagoras theorem

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: hypotenuse {}^{2} = base {}^{2} + height {}^{2} }}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: \: l(cb) {}^{2} = l(pb) {}^{2} + l( cp) {}^{2} }}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: l(10) {}^{2} + l(6) {}^{2} + l(cp) {}^{2} }}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies100 = 36 - l(cp) {}^{2} }}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: l(cp) { }^{2} = 100 - 36 }}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: l(cp) {}^{2} = 64 }}}}}\\ \\\end{gathered}$

$\begin{gathered}\qquad\qquad{\underline{\underline{\frak{\pink{\implies \: l(cp) = 8cm \: }}}}}\\ \\\end{gathered}$

Therefore , Diameter of the circle = 8cm

___________________________

$\dagger \underline{\large \: \: {\frak{Points \: to \: remember : }}}$

• The perpendicular drawn from the centre of the circle to its chord bisects the chord.
• The segment joining the centre of the circle and midpoint of its chord is perpendicular to the chord.
• Basically a chord is a line segment which joints two points in the circle.

Rules for phythagoras theorem :

• Phythagoras theorem states that the square on the hypotenuse is equal to the sum of squares on the other two sides.
• The hypotenuse is a longest side and it's always opposite to right angle.
• Phythagoras theorem is only used in right angeled triangle because only right angled triangle contains base , height and hypotenuse.