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Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection. - Mathematics

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Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

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Solution

Let two circles having their centres as O and O' intersect each other at point A and B respectively. Let us join OO'.

In ΔAOO' and BOO',

OA = OB (Radius of circle 1)

O'A = O'B (Radius of circle 2)

OO' = OO' (Common)

ΔAOO' ≅ ΔBOO' (By SSS congruence rule)

∠OAO' = ∠OBO' (By CPCT)

Therefore, line of centres of two intersecting circles subtends equal angles at the two points of intersection.

Concept: Cyclic Quadrilateral
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APPEARS IN

NCERT Class 9 Maths
Chapter 10 Circles
Exercise 10.6 | Q 1 | Page 186

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