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

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

Write 'True' or 'False' and give reasons for your answer.
The tangent to the circumcircle of an isosceles triangle $ABC$ at $A$,in which $AB = AC$,is parallel to $BC$.

Points $A$ and $B$ are distinct points on $\odot(O, r)$ and point $C$ on the circle lies in the interior of $\angle AOB$. Then,$\overline{AB} \cup \widehat{ACB}$ is ........

$\overline{PA}$ is a tangent to $\odot(O, r)$ drawn from a point $P$ outside a circle. If $m\angle AOP = 40^\circ$,then $m\angle OPA = \ldots$ (in $^\circ$)

$A$ tangent $\stackrel{\leftrightarrow}{AB}$ of $\odot(P, r)$ touches the circle at $Q$. If a perpendicular is drawn from $P$ onto $AB$,then the foot of the perpendicular is ....

Vedclass Test Series

Exam Paper Generator

Online Exam Module