Two concentric circles are of radii 5 , cm an | vedclass

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

Question

(C) Let the two concentric circles be centered at point $O$. Let $PQ$ be the chord of the larger circle which touches the smaller circle at point $A$.

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) Let the two concentric circles be centered at point $O$. Let $PQ$ be the chord of the larger circle which touches the smaller circle at point $A$. Therefore,$PQ$ is tangent to the smaller circle at point $A$.Since $OA$ is the radius of the smaller circle and $PQ$ is the tangent,$OA \perp PQ$.Applying the Pythagoras theorem in $	riangle OAP$,we have:$OA^2 + AP^2 = OP^2$$3^2 + AP^2 = 5^2$$9 + AP^2 = 25$$AP^2 = 25 - 9 = 16$$AP = \sqrt{16} = 4 \, cm$.Since the perpendicular from the center of a circle to a chord bisects the chord,we have $AP = AQ$.Therefore,the length of the chord $PQ = AP + AQ = 2 	imes AP = 2 	imes 4 = 8 \, cm$.

Two concentric circles are of radii $5 \, cm$ and $3 \, cm$. Find the length of the chord of the larger circle which touches the smaller circle.

Similar Questions

Prove that in two concentric circles,the chord of the larger circle,which touches the smaller circle,is bisected at the point of contact.

Fill in the blanks:
$(i)$ $A$ circle can have $......$ parallel tangents at the most.
$(ii)$ The common point of a tangent to a circle and the circle is called $......$

From a point $Q$,the length of the tangent to a circle is $24 \, cm$ and the distance of $Q$ from the centre is $25 \, cm$. The radius of the circle is (in $cm$)

Prove that the parallelogram circumscribing a circle is a rhombus.

$A$ tangent $PQ$ at a point $P$ of a circle of radius $5 \, cm$ meets a line through the centre $O$ at a point $Q$ so that $OQ = 12 \, cm$. The length of $PQ$ is (in $cm$):

Vedclass Test Series

Exam Paper Generator

Online Exam Module