Q) Prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals.

9th Class Maths – NCERT Important Questions

Ans:

Step 1:

Let’s make a diagram for better understanding of the question:

Here, AB is the side of a rhombus and also diameter of the circle.

Diagonals of Rhombus are intersecting each other at point O.

We need to prove that point O lies on the circle.

Step 2:

We know that the diagonals of the Rhombus cut each other at 90 ⁰

∴  ∠ AOB = 90 ⁰

Step 3:

We know that the diameter of a circle subtends 90 ⁰ on any point of the circle.

Alternatively, if diameter is subtending 90 ⁰ at any point, then that point lies on the circle.

∵ ∠ AOB = 90 ⁰

∴ Point O lies on the circle…. Hence Proved !

Therefore, the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals.

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