At one end A of a diameter AB of a circle of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the circle have center $O$ and radius $r = 5 \, cm$. $AB$ is a diameter,so $OA = OB = 5 \, cm$.Tangent $XY$ is drawn at point $A$. Since the t

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(D) Let the circle have center $O$ and radius $r = 5 \, cm$. $AB$ is a diameter,so $OA = OB = 5 \, cm$.Tangent $XY$ is drawn at point $A$. Since the tangent at any point of a circle is perpendicular to the radius through the point of contact,$OA \perp XY$.Let the chord $CD$ be parallel to $XY$. Let $CD$ intersect the diameter $AB$ at point $E$. Since $CD \parallel XY$ and $OA \perp XY$,it follows that $OE \perp CD$.The distance of the chord $CD$ from $A$ is given as $AE = 8 \, cm$.Since $OA = 5 \, cm$,the distance of the chord from the center $O$ is $OE = AE - OA = 8 - 5 = 3 \, cm$.In the right-angled triangle $	riangle OEC$,by the Pythagorean theorem:$OC^2 = OE^2 + EC^2$$5^2 = 3^2 + EC^2$$25 = 9 + EC^2$$EC^2 = 16$$EC = 4 \, cm$.Since the perpendicular from the center to a chord bisects the chord,$CD = 2 	imes EC = 2 	imes 4 = 8 \, cm$.

At one end $A$ of a diameter $AB$ of a circle of radius $5 \, cm$,a tangent $XY$ is drawn to the circle. The length of the chord $CD$ parallel to $XY$ and at a distance of $8 \, cm$ from $A$ is (in $cm$):

Similar Questions

The chord of $\odot(O, 34)$ touches $\odot(O, 16)$. The length of the chord is .........

In the given figure,$AT$ is a tangent to the circle with center $O$ such that $OT = 4 \, cm$ and $\angle OTA = 30^{\circ}$. Then $AT$ is equal to (in $cm$):

In the figure,common tangents $AB$ and $CD$ to two circles intersect at $E$. Prove that $AB = CD$.

$P$ lies in the exterior of $\odot(O, 8)$ such that $OP = 17$. Two tangents are drawn to the circle which touch the circle at $A$ and $B$. Find $AB$.

Two concentric circles having radii $17$ and $8$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.

Vedclass Test Series

Exam Paper Generator

Online Exam Module