Out of two concentric circles,the radius of t | vedclass

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

Question

(D) Let $C_1$ and $C_2$ be the circles having the same centre $O$. $AC$ is a chord of the outer circle $C_2$ which touches the inner circle $C_1$ at p

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) Let $C_1$ and $C_2$ be the circles having the same centre $O$. $AC$ is a chord of the outer circle $C_2$ which touches the inner circle $C_1$ at point $D$.Join $OD$.Since $AC$ is a tangent to the inner circle at $D$,$OD \perp AC$.$A$ perpendicular drawn from the centre to a chord bisects the chord.Therefore,$AD = DC = \frac{8}{2} = 4 \, cm$.In the right-angled $	riangle AOD$,by Pythagoras theorem:$OA^2 = AD^2 + OD^2$$5^2 = 4^2 + OD^2$$25 = 16 + OD^2$$OD^2 = 25 - 16 = 9$$OD = \sqrt{9} = 3 \, cm$.Thus,the radius of the inner circle is $3 \, cm$.

Out of two concentric circles,the radius of the outer circle is $5 \, cm$ and the chord $AC$ of length $8 \, cm$ is a tangent to the inner circle. Find the radius of the inner circle (in $cm$).

Similar Questions

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.

$P$ is a point in the exterior of a circle having centre $O$ and radius $21$. $OP = 25$. $A$ tangent from $P$ touches the circle at $Q$. Find $PQ$.

State whether the following statement is 'True' or 'False' and provide reasons for your answer: The length of a tangent from an external point to a circle is always greater than the radius of the circle.

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

$P$ is a point in the exterior of $\odot(O, r)$ and the tangents from $P$ to the circle touch the circle at $X$ and $Y$. Find $OP$,if $r = 12$ and $XP = 5$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module