In a circle with centre P,the distance of a c | vedclass

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

Question

(A) Let $P$ be the centre of the circle and $AB$ be the chord. Let $M$ be the midpoint of the chord $AB$ such that $PM \perp AB$. Given that the dista

Vedclass · Accepted Answer

$52$

Vedclass · Answer

(A) Let $P$ be the centre of the circle and $AB$ be the chord. Let $M$ be the midpoint of the chord $AB$ such that $PM \perp AB$. Given that the distance of the chord from the centre is $PM = 20 \, cm$. The length of the chord $AB = 96 \, cm$. Since the perpendicular from the centre to a chord bisects the chord,we have $AM = MB = \frac{AB}{2} = \frac{96}{2} = 48 \, cm$. In the right-angled triangle $	riangle PMA$,by the Pythagorean theorem,$PA^2 = PM^2 + AM^2$. Here,$PA$ is the radius $(r)$ of the circle. $r^2 = 20^2 + 48^2$. $r^2 = 400 + 2304 = 2704$. $r = \sqrt{2704} = 52 \, cm$. Thus,the radius of the circle is $52 \, cm$.

In a circle with centre $P$,the distance of a chord $AB$ from the centre $P$ is $20 \, cm$. If $AB = 96 \, cm$,then the radius of the circle is .......... $cm$.

Similar Questions

In a circle with centre $P$,$AB$ is a chord and point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB + \angle APB = 150^{\circ}$,then find $\angle APB$. (in $^{\circ}$)

Write True or False and justify your answer.
The angles subtended by a chord at any two points of a circle are equal.

In cyclic quadrilateral $ABCD$,if $5 \angle A = 13 \angle C$,then find $\angle A$. (in $^{\circ}$)

State whether each of the following statements is true or false:
$(1)$ There are three circles passing through three given non-collinear points.
$(2)$ Infinitely many circles pass through two given points.

Prove that if chords of congruent circles subtend equal angles at their centres,then the chords are equal.

Vedclass Test Series

Exam Paper Generator

Online Exam Module