Two concentric circles of radii 73cm and 55cm. find the length of the chord of the larger circle which touches the smaller circle.
Last updated date: 20th Mar 2023
•
Total views: 307.2k
•
Views today: 8.85k
Answer
307.2k+ views
Hint: - Perpendicular drawn from the center to the chord of the circle bisects the chord.
Two concentric circles of radii 55cm and 73cm are shown in figure.
$ \Rightarrow {\text{OA = 55cm and OP = 73cm}}$
Now we have to find out the chord of the larger circle which touches the smaller circle.
$ \Rightarrow $So, from the figure we have to find out the value of PQ.
Since OA is perpendicular on the chord PQ, therefore triangle OAP is a right angle triangle at A
So, apply Pythagoras Theorem in triangle OAP, we have
$
{\text{O}}{{\text{A}}^2}{\text{ + A}}{{\text{P}}^2}{\text{ = O}}{{\text{P}}^2} \\
\Rightarrow {\text{A}}{{\text{P}}^2} = {73^2} - {55^2} \\
\Rightarrow {\text{A}}{{\text{P}}^2} = 5329 - 3025 = 2304 \\
\Rightarrow {\text{AP = 48cm}} \\
$
As we know that the perpendicular drawn from the center to the chord of the circle bisects the chord.
$\therefore {\text{PQ = 2AP = 2}} \times 48 = 96cm$
So, the length of the chord which touches the smaller circle is 96 cm.
Note: - Concentric circles are the circles with a common center and whenever we face such types of problem first draw the pictorial representation then draw the perpendicular from the center on the chord of the circle which divide the chord into two equal parts, then apply Pythagoras Theorem we will get the required answer.

Two concentric circles of radii 55cm and 73cm are shown in figure.
$ \Rightarrow {\text{OA = 55cm and OP = 73cm}}$
Now we have to find out the chord of the larger circle which touches the smaller circle.
$ \Rightarrow $So, from the figure we have to find out the value of PQ.
Since OA is perpendicular on the chord PQ, therefore triangle OAP is a right angle triangle at A
So, apply Pythagoras Theorem in triangle OAP, we have
$
{\text{O}}{{\text{A}}^2}{\text{ + A}}{{\text{P}}^2}{\text{ = O}}{{\text{P}}^2} \\
\Rightarrow {\text{A}}{{\text{P}}^2} = {73^2} - {55^2} \\
\Rightarrow {\text{A}}{{\text{P}}^2} = 5329 - 3025 = 2304 \\
\Rightarrow {\text{AP = 48cm}} \\
$
As we know that the perpendicular drawn from the center to the chord of the circle bisects the chord.
$\therefore {\text{PQ = 2AP = 2}} \times 48 = 96cm$
So, the length of the chord which touches the smaller circle is 96 cm.
Note: - Concentric circles are the circles with a common center and whenever we face such types of problem first draw the pictorial representation then draw the perpendicular from the center on the chord of the circle which divide the chord into two equal parts, then apply Pythagoras Theorem we will get the required answer.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
