Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Text Solution
Verified by Experts
By pythagoras theorem,
`OA^2 = AP^2 + OP^2`
In `/_\BPO`
`OB^2 = BP^2 + OP^2`
from above we get
`AP = BP`
...
Topper's Solved these Questions
CIRCLES
NCERT ENGLISH|Exercise Exercise 10.1|2 Videos
ARITHMETIC PROGRESSIONS
NCERT ENGLISH|Exercise All Questions|65 Videos
CONSTRUCTIONS
NCERT ENGLISH|Exercise EXERCISE 11.2|7 Videos
Similar Questions
Explore conceptually related problems
In two concentric circle, prove that a chord of larger circle which is tangent to smaller circle is bisected at the point of contact.
In two concentric circles prove that all chords of the outer circle which touch the inner circle are of equal length.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Two concentric circles are of radii 5 cm. and 3 c. Find the length of the chord of the larger circle which touches the cmaller circle.
The shows two concentric circles and AD is a chord of lenger circle. prove that AB=CD
Find the area of the region between the two concentric circles, if the length of a chord of the outer circle just touching the inner circle at a particular point on it is 10 cm (Take, pi = (22)/(7) )
In the adjoining figure, O is the centre of two concentric circles. The chord AB of larger circle intersects the smaller circle at C and D. (i) Find AC:BD . (ii) If AC=2cm , then find the length of BD.
The locus of the centre of a circle which touches two given circles externally is a
