Question

if two equal chords of a circle intersect within the circle prove that the line joining the point of intersecting to the centre make equal angle with the chords

Answer 1

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Answer 2

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Solution:

Let's suppose that we have circle with centre O. There are two equal chords AB and CD intersecting at point E.

Construction: Draw OM⊥AB and ON⊥CD. Join OE.

We need to prove that ∠OEM=∠OEN

In ∆OME and ∆ONE, we have

∠OME=∠ONE        (Each equal to 90°)

OE=OE                        (Common)

OM=ON             (Equal chords are equidistant from the centre)

Therefore, by RHS congruence rule, we have ∆OME≅∆ONE

⇒∠OEM=∠OEN         (Corresponding parts of congruent triangles are equal)

hope, this will help you.

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