Answer

Verified

352.9k+ views

Hint – Length of the lines joining the end points of chords of a circle to the centre of a circle are radius , Thus the triangle formed here is the right angle isosceles triangle (given) . Clearly PGT can be used here .

The pictorial representation of the given problem is shown above.

Let AB be the chord of the circle.

O is the center of the circle, chord AB subtends a right angle at its center.

$\therefore \angle AOB = {90^0}$

OA = OB = 10 cm radius of the circle.

Now we have to find out the length of the chord AB.

So, apply Pythagoras theorem in triangle AOB

$

\Rightarrow {\left( {{\text{Hypotenuse}}} \right)^2} = {\left( {{\text{Base}}} \right)^2} + {\left( {{\text{Perpendicular}}} \right)^2} \\

\Rightarrow {\left( {AB} \right)^2} = {\left( {OB} \right)^2} + {\left( {OA} \right)^2} \\

\Rightarrow {\left( {AB} \right)^2} = {10^2} + {10^2} = 100 + 100 = 200 \\

\Rightarrow AB = \sqrt {200} = 10\sqrt 2 {\text{ cm}} \\

$

So, the length of the chord is $10\sqrt 2 {\text{ cm}}$.

Hence, option (b) is correct.

Note – In such types of questions first draw the pictorial representation of the given problem as above then always remember the property of Pythagoras Theorem which is stated above, then using this property calculate the length of the chord which is the required answer.

The pictorial representation of the given problem is shown above.

Let AB be the chord of the circle.

O is the center of the circle, chord AB subtends a right angle at its center.

$\therefore \angle AOB = {90^0}$

OA = OB = 10 cm radius of the circle.

Now we have to find out the length of the chord AB.

So, apply Pythagoras theorem in triangle AOB

$

\Rightarrow {\left( {{\text{Hypotenuse}}} \right)^2} = {\left( {{\text{Base}}} \right)^2} + {\left( {{\text{Perpendicular}}} \right)^2} \\

\Rightarrow {\left( {AB} \right)^2} = {\left( {OB} \right)^2} + {\left( {OA} \right)^2} \\

\Rightarrow {\left( {AB} \right)^2} = {10^2} + {10^2} = 100 + 100 = 200 \\

\Rightarrow AB = \sqrt {200} = 10\sqrt 2 {\text{ cm}} \\

$

So, the length of the chord is $10\sqrt 2 {\text{ cm}}$.

Hence, option (b) is correct.

Note – In such types of questions first draw the pictorial representation of the given problem as above then always remember the property of Pythagoras Theorem which is stated above, then using this property calculate the length of the chord which is the required answer.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE