Question : In the given figure, $\mathrm{MNOP}$ is a square of side $6\;\mathrm{cm}$. What is the value (in $\mathrm{cm}$) of the radius of a circle?

Option 1: $4.25$
Option 2: $3.75$
Option 3: $3.5$
Option 4: $4.55$

Question

Question : In the given figure, $\mathrm{MNOP}$ is a square of side $6\;\mathrm{cm}$. What is the value (in $\mathrm{cm}$) of the radius of a circle?

Option 1: $4.25$

Option 2: $3.75$

Option 3: $3.5$

Option 4: $4.55$

Team Careers360 · Accepted Answer

Correct Answer: $3.75$

Solution :

Given that $\mathrm{MNOP}$ is a square of side $6\;\mathrm{cm}$.
Construction: Join $\mathrm{QC}$ and $\mathrm{PC}$.
$\mathrm{OT = \frac{ON}{2} = 3\;\mathrm{cm}}$
$\mathrm{OP = 6\;\mathrm{cm}}$
$\mathrm{OT^2 = OR imes OP}$
$\mathrm{3^2 = OR imes 6}$
⇒ $\mathrm{OR = \frac{9}{6} = \frac{3}{2}\;\mathrm{cm}}$
$\mathrm{PR = OP - OR}$
$ \mathrm{PR = 6 - \frac{3}{2} = \frac{9}{2}\;\mathrm{cm}}$
$\mathrm{PQ = \frac{1}{2}× \frac{9}{2} = \frac{9}{4}\;\mathrm{cm}}$
$\mathrm{QC = \frac{1}{2} × 6 = 3\;\mathrm{cm}}$
Applying the Pythagorean theorem in $ riangle \mathrm{PQC}$,
$\mathrm{PC^2 = PQ^2 + QC^2}$
⇒ $\mathrm{ PC^2 = \left(\frac{9}{4} ight)^2 + 3^2 = \frac{225}{16}⇒ \mathrm{PC}= \frac{15}{4} = 3.75}\;\mathrm{cm}$
Hence, the correct answer is $3.75$.

Popular Searches

Question : In the given figure, $\mathrm{MNOP}$ is a square of side $6\;\mathrm{cm}$. What is the value (in $\mathrm{cm}$) of the radius of a circle?

Option 1: $4.25$
Option 2: $3.75$
Option 3: $3.5$
Option 4: $4.55$

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Popular Searches

Question : In the given figure, $\mathrm{MNOP}$ is a square of side $6\;\mathrm{cm}$. What is the value (in $\mathrm{cm}$) of the radius of a circle? Option 1: $4.25$Option 2: $3.75$Option 3: $3.5$Option 4: $4.55$

Related Questions

Question : The area of the square inscribed in a circle of radius 8 cm is:Option 1: $256\;\mathrm{cm^2}$Option 2: $250\;\mathrm{cm^2}$Option 3: $128\;\mathrm{cm^2}$Option 4: $125\;\mathrm{cm^2}$

Question : The area of a sector of a circle is 88 sq. cm., and the angle of the sector is 45°. Find the radius of the circle. (Use $\pi=\frac{22}{7}$)Option 1: $3 \sqrt{ 11} \mathrm{~cm}$Option 2: $4 \sqrt{ 14} \mathrm{~cm}$Option 3: $6 \sqrt{ 13} \mathrm{~cm}$Option 4: $5 \sqrt{ 14} \mathrm{~cm}$

Question : What is the perimeter of a square inscribed in a circle of radius 5 cm?Option 1: $20 \sqrt{2}\ \mathrm{~cm}$Option 2: $40\sqrt{2}\ \mathrm{~cm}$Option 3: $30\sqrt{2}\ \mathrm{~cm}$Option 4: $10\sqrt{2}\ \mathrm{~cm}$

Question : The area of a sector of a circle is 66 cm2 and the angle of the sector is 60°. Find the radius of the circle.Option 1: $5 \sqrt{15} \mathrm{~cm}$Option 2: $6 \sqrt{14} \mathrm{~cm}$Option 3: $7 \sqrt{19} \mathrm{~cm} $Option 4: $3 \sqrt{14} \mathrm{~cm} $