Question

If two equal chords of a circle
intersect within the circle, prove that the line joining the point, of
intersection to the centre makes equal angles with the chords.

Answer 1

Hi there!

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For solutions, Refer to the attached picture.
Regrets for handwriting _/\_

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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.

⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.

⚫ Secant : A line intersecting a circle at any two points, is called secant.

⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.

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Answer 2

Hello mate =_=

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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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