In a circle with centre P,the diameter of the | vedclass

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

Question

(B) Given: Diameter of the circle $d = 70 \, cm$. Radius $r = \frac{d}{2} = \frac{70}{2} = 35 \, cm$. Let $M$ be the midpoint of chord $AB$ such that

Vedclass · Accepted Answer

$56$

Vedclass · Answer

(B) Given: Diameter of the circle $d = 70 \, cm$. Radius $r = \frac{d}{2} = \frac{70}{2} = 35 \, cm$. Let $M$ be the midpoint of chord $AB$ such that $PM \perp AB$. The distance from the centre to the chord is $PM = 21 \, cm$. In right-angled triangle $	riangle PMA$,by Pythagoras theorem: $PA^2 = PM^2 + AM^2$ $35^2 = 21^2 + AM^2$ $1225 = 441 + AM^2$ $AM^2 = 1225 - 441 = 784$ $AM = \sqrt{784} = 28 \, cm$. Since the perpendicular from the centre to a chord bisects the chord,$AB = 2 	imes AM = 2 	imes 28 = 56 \, cm$.

In a circle with centre $P$,the diameter of the circle is $70 \, cm$. The chord $AB$ is at a distance of $21 \, cm$ from the centre of the circle,then $AB = \dots \, cm$.

Similar Questions

In the figure,$OD$ is perpendicular to chord $AB$ of a circle whose centre is $O.$ If $BC$ is a diameter,prove that $CA = 2OD$.

Suppose you are given a circle. Give a construction to find its centre.

$A$ line joining the midpoints of two chords passes through the centre of a circle. Prove that the chords are parallel.

In the figure,if $OA = 5 \text{ cm}$,$AB = 8 \text{ cm}$,and $OD$ is perpendicular to $AB$,then $CD$ is equal to (in $\text{cm}$):

If a line segment joining the mid-points of two chords of a circle passes through the centre of the circle,prove that the two chords are parallel.

Vedclass Test Series

Exam Paper Generator

Online Exam Module