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 angle with the chords

Answer 1

HEY MATE!

Join OP, draw OL ⟂ AB and OM ⟂ CD, thus, L and M are  the mid - points of AB and CD respectively. Also, equal chords are equidistant from the centre . 

∴ OL = OM 

Now, in right - angled △s OLP and OMP     

OL = OM 

OP = OP [common]

∠OLP = ∠OMP [each = 90°]

So, by RHS congruence axiom, we have 

△OLP ≅  △OMP 

Hence, ∠OLP = ∠OMP   [c.p.c.t.] 

I HOPE IT HELPS YOU!

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.

Thank you______❤

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