Question

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

Answer 1

Answer:

Step-by-step explanation:

❣Holla user❣

Here is ur ans⬇️⬇️⬇️

Let AB and CD are the two equal chords of a circle having center O

Again let AB and CD intersect each other at a point M.

Now, draw OP perpendicular AB and OQ perpendicular CD

From the figure,

In ΔOPM and ΔOQM,

OP = OQ {equal chords are equally distant from the cntre}

∠OPM = ∠OQM

OM = OM {common}

By SAS congruence criterion,

ΔOPM ≅ ΔOQM

So, ∠OMA = ∠OMD

or ∠OMP = ∠OMQ {by CPCT}

Thus, the line joining the point of intersection to the center makes equal angles with the chords.

Referred the figure given below⬇️⬇️⬇️

Hope it helps u^_^

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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