Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Q.

A right angled isosceles triangle is inscribed in a circle of radius $r$ . What is the area of the remaining portion of the circle?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

a

\frac{π r^{2}}{2}

b

(π - \frac{1}{2}) r^{2}

c

(π - 1) r^{2}

d

(π - 2) r^{2}

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given, a right angled isosceles triangle is inscribed in a circle of radius

r

.

Question Image

Let r be the radius of the circle and a be the length of the sides that contain the right angle. The diameter of the circle is the hypotenuse of a right-angled triangle.
Pythagoras theorem states that the square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides.
So, by applying pythagoras theorem,

a^{2} + a^{2} = {(2 r)}^{2}

.

\Rightarrow 2 a^{2} = 4 r^{2}

\Rightarrow a = \sqrt{2} r

∴

Remaining area = Area of circle

-

Area of triangle.
We know that area of a circle is

π r^{2}

and area of the triangle=

\frac{1}{2} (Base) (Height)

.

\Rightarrow

Remaining area

= π r^{2} - \frac{1}{2} (r \sqrt{2}) (r \sqrt{2})

.

\Rightarrow

Remaining area

= π r^{2} - r^{2}

\Rightarrow

Remaining area

= r^{2} (π - 1)

Hence, option 3 is correct.

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

Not sure what to do in the future? Don’t worry! We have a FREE career guidance session just for you!

A right angled isosceles triangle is inscribed in a circle of radius r. What is the area of the remaining portion of the circle?