#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# IF TWO EQUAL CHORDS OF A CIRCLE INTERSECT WITHIN THE CIRCLE,PROVE THAT THE SEGMENTS OF THE CHORD ARE EQUAL TO THE CORRESPONDING SEGMENTS OF THE OTHER CHORD.

Arun
25763 Points
3 years ago

Given:  Let PQ and RS be two equal chords of a given circle and they are intersecting each other at point T.

To prove: PT = RT and ST = QT

Construction: Draw OV PQ and OU  SR. Join OT.

Proof: In ΔOVT and ΔOUT,

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

OT = OT      (Common )

∴ ΔOVT ≅ ΔOUT          ( R.H.S.)

⇒ VT= UT                  (By CPCT )

⇒ PV + VT = RU + UT  (∵ AV = RU = ( ½ )PQ = (½) RS

⇒ PT = RT

⇒ PQ – PT = SR – RT     (Given PQ = RS )

⇒ QT= ST.