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

Solution:

Draw two intersecting circles with centers O and O’, respectively. Join these two centers. Let the points of intersection be A and B.

We need to prove that ∠OAO'= ∠OBO'

Consider ΔOAO’ and ΔOBO’

OA = OB (Radii of a circle with center O)

O’A = O’B (Radii of a circle with center O’)

OO’= OO’ (Common)

Therefore, by SSS criteria, ΔOAO’ and ΔOBO’ are congruent to each other.

By CPCT, ∠OAO'= ∠OBO'

Hence it is proved that the line of centers of two intersecting circles subtends equal angles at the two points of intersection.

☛ Check: NCERT Solutions Class 9 Maths Chapter 10

Video Solution:

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

Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.6 Question 1:

Summary:

We have proved that the line of centers of two intersecting circles subtends equal angles at the two points of intersection.

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