MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Angle Subtended by an Arc of a Circle on the Circle and at the Center

Two concentri...

Question

Two concentric circles with centre $C$ have radii $r_{1}$ and $r_{2}$ such that $(r_{2} - r_{1}) > 0$ . $C A$ and $C B$ are the common lined radii of the circles. If tangent at $A$ is drawn to meet the bigger circle in the point $D$ . Then the length $B D$ is given by

A

\sqrt{2 r_{1} (r_{2} - r_{1})}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\sqrt{2 r_{2} (r_{2} - r_{1})}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

\sqrt{2 r_{1} (r_{2} + r_{1})}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\sqrt{2 r_{2} (r_{2} + r_{1})}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\sqrt{2 r_{2} (r_{2} - r_{1})}$
$A B = r_{2} - r_{1}$
From $△ D C A, ∠ D A C = 90^{o}$
$\Rightarrow D A = \sqrt{r_{2}^{2} - r_{1}^{2}}$
From $△ D A B, ∠ D A B = 90^{o}$
$\Rightarrow B D = \sqrt{r_{2}^{2} - r_{1}^{2} + {(r_{2} - r_{1})}^{2}}$
$\Rightarrow B D = \sqrt{r_{2}^{2} - r_{1}^{2} + r_{2}^{2} + r_{1}^{2} - 2 r_{1} r_{2}} = \sqrt{2 r_{2} (r_{2} - r_{1})}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Three circles of radii

r_{1}

r_{2}

r_{3}

are drawn concentric to each other. The radii

r_{1}

r_{2}

are such that the area of the circle with radius

r_{1}

is equal to the area between the circles of radii

r_{2}

r_{1}

. The area between the circles of radii

r_{3}

r_{2}

is equal to the area between the circles of radii

r_{2}

r_{1}

What is the value of

r_{1} : r_{2} : r_{3}

?

Q. Three circles of radii

r_{1}, r_{2}

r_{3}

are drawn concentric to each other. The radii

r_{1}

r_{2}

are such that the area of the circle with radius

r_{1}

is equal to the area between the circles of radius

r_{2}

r_{1}

. The area between the circles of radii

r_{3}

r_{2}

is equal to area between the circles of radii

r_{2}

r_{r}

. What is the value of

r_{1} : r_{2} : r_{3} ?

Q. The area between two concentric circles of radii

r_{1}

r_{2},

r_{2} > r_{1}

]

Q. What is the condition for two concentric circles of radii

r_{1}

r_{2}

to be congruent ?

The radii of two concentric circles spherical conducting shells are r1 and r2 (r1<r2) .The change on the outer shell is q. The charge on the inner shell which is connected to the earth is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Circles and Quadrilaterals - Theorem 8

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Angle Subtended by an Arc of a Circle on the Circle and at the Center

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon