Question

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

Answer 1

Given : Let AB and CD are two equal chords of a given circle and they are intersecting each other at point E

To prove : ∠MEO =∠NEO

Construction : Draw perpendiculars OM and ON on AB and CD respectively.

Proof :
In ΔMEO and ΔNEO,

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

∠OME = ∠ONE (Each 90°)

EO = EO (Common)

∴ ΔMEO ≅ ΔNEO [R.H.S congruence rule]

∴ ∠ MEO= ∠ NEO [ CPCT ]

Hence proved.

Answer 2

Hello mate =_=

____________________________

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______❤

_____________________________❤