If the diagram, D C is a diameter of the large circle centered at A, and A C is a diameter of the smaller circle centered at B. If D E is tangent to the smaller circle at F and D C=12 then the length of D E is

Question

If the diagram, D C is a diameter of the large circle centered at A, and A C is a diameter of the smaller circle centered at B. If D E is tangent to the smaller circle at F and D C=12 then the length of D E is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

sin α=(3/9)=(1/3) also sin α=(x/12) (where E C=x ) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6145368fddda97d66dc3aa3073db162e-.png" /> (1/3)=(x/12) ⇒ x=4 (D E)2=144-16=128 ⇒ D E=8 √2

Q. If the diagram, $D C$ is a diameter of the large circle centered at $A$ , and $A C$ is a diameter of the smaller circle centered at $B$ . If $D E$ is tangent to the smaller circle at $F$ and $D C = 12$ then the length of $D E$ is

$sin α = \frac{3}{9} = \frac{1}{3}$
also $sin α = \frac{x}{12}$
(where $EC = x$ )

$\frac{1}{3} = \frac{x}{12} \Rightarrow x = 4$
$(D E)^{2} = 144 - 16 = 128$
$\Rightarrow D E = 82$

Q. If the diagram, DC is a diameter of the large circle centered at A, and AC is a diameter of the smaller circle centered at B. If DE is tangent to the smaller circle at F and DC=12 then the length of DE is

sinα=93​=31​ also sinα=12x​ (where EC=x ) 31​=12x​⇒x=4 (DE)2=144−16=128 ⇒DE=82​

Q. If the diagram, $D C$ is a diameter of the large circle centered at $A$ , and $A C$ is a diameter of the smaller circle centered at $B$ . If $D E$ is tangent to the smaller circle at $F$ and $D C = 12$ then the length of $D E$ is

$sin α = \frac{3}{9} = \frac{1}{3}$
also $sin α = \frac{x}{12}$
(where $EC = x$ )

$\frac{1}{3} = \frac{x}{12} \Rightarrow x = 4$
$(D E)^{2} = 144 - 16 = 128$
$\Rightarrow D E = 82$