Question

if two cords of a circle intersect within the circle , provethatthe line joining the point of intersection to the centre makes equal angles with in the cords .​

Answer 1

Answer:

ok The circumference of a circle is 2πr or πD if diameter is given.

The answer is 25.13 cm

Step-by-step explanation:

Now method 1:

C=2πr

So finding for radius in this equation=diameter/2

8/2=4 cm

So now 2 × 22/7 × 4

176/7=25.13 cm

OR

C=πD

22/7 × 8

176/7=25.13 cm

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Answer 2

Answer:

SEE THE PICTURE FOR THE LINE SEGMENTS

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.