Question
In figure, the chord of the larger of the two concentric circles, with centre touches the smaller circle at Prove that
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Text solutionVerified
Given: Two concentric circles and with centre O, and AB is the chord of touching at
To prove:
Construction: Join
Proof: is the chord of touching at then is the tangent to at with as its radius.
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Therefore,
Considering, as the chord of the circle . So, .
Therefore, is the bisector of the chord
Hence, (Perpendicular from the centre to the chord bisects the chord).
To prove:
Construction: Join
Proof: is the chord of touching at then is the tangent to at with as its radius.
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Therefore,
Considering, as the chord of the circle . So, .
Therefore, is the bisector of the chord
Hence, (Perpendicular from the centre to the chord bisects the chord).
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Question Text | In figure, the chord of the larger of the two concentric circles, with centre touches the smaller circle at Prove that |
Answer Type | Text solution:1 |
Upvotes | 150 |