In a circle with centre P,the length of a dia | vedclass

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

Question

(B) Given that the diameter of the circle is $20 \, cm$,the radius $r = \frac{20}{2} = 10 \, cm$.Let $M$ be the midpoint of the chord $AB$ such that $

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(B) Given that the diameter of the circle is $20 \, cm$,the radius $r = \frac{20}{2} = 10 \, cm$.Let $M$ be the midpoint of the chord $AB$ such that $PM \perp AB$. The distance from the centre $P$ to the chord $AB$ is $PM = 6 \, cm$.In the right-angled triangle $	riangle PMA$,by the Pythagorean theorem:$PA^2 = PM^2 + AM^2$$10^2 = 6^2 + AM^2$$100 = 36 + AM^2$$AM^2 = 100 - 36 = 64$$AM = \sqrt{64} = 8 \, cm$.Since the perpendicular from the centre to a chord bisects the chord,$AB = 2 	imes AM = 2 	imes 8 = 16 \, cm$.

In a circle with centre $P$,the length of a diameter is $20 \, cm$ and $AB$ is a chord of a circle at a distance $6 \, cm$ from the centre,then $AB = $ ........ $cm$.

Similar Questions

Write True or False and justify your answer in each of the following: Two chords $AB$ and $CD$ of a circle are each at distances $4 \ cm$ from the centre. Then $AB = CD$.

In the figure,$\angle ACB = 40^{\circ}$. Find $\angle OAB$.

If $BM$ and $CN$ are the altitudes drawn on the sides $AC$ and $AB$ of the triangle $ABC$,prove that the points $B, C, M$ and $N$ are concyclic.

In a circle with centre $P$,$AB$ is a diameter and $ABCD$ is a cyclic quadrilateral. If $\angle ADC = 150^{\circ}$,then find $\angle BAC$. (in $^{\circ}$)

$P$ is the centre of the circle of radius $20\, cm$. $AB$ is a chord of the circle. If $AB = 32\, cm$,then find the distance of the chord $AB$ from the centre $P$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module