A B is a diameter of a circle. C D is a chord parallel to A B and 2 C D=A B. The tangent at B meets the line A C produced at E and A E=K ⋅ A B, then K is equal to

Question

A B is a diameter of a circle. C D is a chord parallel to A B and 2 C D=A B. The tangent at B meets the line A C produced at E and A E=K ⋅ A B, then K is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x2+y2=4 a2 (-a, a √3) ; tan θ=(a √3/a)=√3 ⇒ θ=60° cos 60°=(4 a/A E) A E=8 a=2 A B <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/07756b67e88404ba27a4802477c1d7e0-.png" />

Q. $A B$ is a diameter of a circle. $C D$ is a chord parallel to $A B$ and $2 C D = A B$ . The tangent at $B$ meets the line $A C$ produced at $E$ and $A E = K \cdot A B$ , then $K$ is equal to

$x^{2} + y^{2} = 4 a^{2}$
$(- a, a 3); tan θ = \frac{a 3}{a} = 3$
$\Rightarrow θ = 6 0^{\circ}$
$cos 6 0^{\circ} = \frac{4 a}{A E}$
$A E = 8 a = 2 A B$

Q. AB is a diameter of a circle. CD is a chord parallel to AB and 2CD=AB. The tangent at B meets the line AC produced at E and AE=K⋅AB, then K is equal to

x2+y2=4a2 (−a,a3​);tanθ=aa3​​=3​ ⇒θ=60∘ cos60∘=AE4a​ AE=8a=2AB

Q. $A B$ is a diameter of a circle. $C D$ is a chord parallel to $A B$ and $2 C D = A B$ . The tangent at $B$ meets the line $A C$ produced at $E$ and $A E = K \cdot A B$ , then $K$ is equal to

$x^{2} + y^{2} = 4 a^{2}$
$(- a, a 3); tan θ = \frac{a 3}{a} = 3$
$\Rightarrow θ = 6 0^{\circ}$
$cos 6 0^{\circ} = \frac{4 a}{A E}$
$A E = 8 a = 2 A B$