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
Answers
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.