Question

two equal chords PQ and Rs of a circle with Centre O when produced meet at a point and prove that q and is equal to SM

Answer 1

you can get the answer from here

Answer 2

Proved below.

Step-by-step explanation:

Given:

Here, we have two equal chords PQ and RS of a circle with center O.

And both the chords when produced meet at a point, let say M.

To prove: QM = SM

Proof:

In Δ AMO and Δ BMO

OA = OB         (equal chords at equidistant from center)

OM = OM        (common)

∠OAM = ∠OBM   (each 90°)

ΔAMO ≅ ΔBMO   ( By SSA criteria)

AM = BM     (By CPCT)

AQ + QM = BS + SM

AB = CD     [ By CPCT ]

so, dividing both the sides by 2

$\frac{1}{2} AB = \frac{1}{2} CD$

AQ = BS

QM = SM

Hence proved.