Question

if two equal chord of a circle intresect within the circle .prove that the segment of one chord are equal to corresponding segments of the others chord ​

Answer 1

Answer:

If two equal chords of a circle intersect within the circle, prove that the segments of

one chord are equal to corresponding segments of the other chord.

Answer:

Let PQ and RS be two equal chords of a given circle and they are intersecting each

other at point T.

Draw perpendiculars OV and OU on these chords.

In ∆OVT and ∆OUT,

OV = OU (Equal chords of a circle are equidistant from the centre)

OVT = OUT (Each 90°)

OT = OT (Common)

∆OVT ∆OUT (RHS congruence rule) VT =

UT (By CPCT) ... (1)

It is given that,

On adding equations (1) and (3), we obtain

PQ = RS ... (2)

PV = RU ... (3)

⇒+ VT = RU + UT

PT = RT ... (4)

On subtracting equation (4) from equation (2), we obtain

PQ − PT = RS − RT

QT = ST ... (5)

Equations (4) and (5) indicate that the corresponding segments of chords PQ and RS

are congruent to each other.