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CBSE Class 9 Mathematics Question 6 of 20

Circles — Question 4

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Question 4

If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.

If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD. NCERT Class 9 Mathematics CBSE Solutions.
Answer

Draw a perpendicular from the center of the circle to the line AD, such that OM ⊥ AD

BC and AD are the chords of smaller circle and the bigger circle respectively.

If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD. NCERT Class 9 Mathematics CBSE Solutions.

We know that,

Perpendicular from the center bisects the chord.

⇒ BM = MC ......... (1)

⇒ AM = MD ......... (2)

By subtracting equation (1) from (2), we get :

⇒ AM − BM = MD − MC

⇒ AB = CD

Hence, proved that AB = CD.