Pls solve this

The equal chords AB and CD of a circle with centre O,when produced,meet at P outside the circle.Prove that 1.PB=PD, 2.PA=PC.

 

Asked by gsitabhanu24 | 31st Jan, 2019, 07:54: PM

Expert Answer:

Angles subtended by equal chords are equal.
So we have AC||BD, alternate angles test.
in triangle APC
BD ||AC
so
By BPT
AB/PB=CD/PD
now
AB=CD
so
PB=PD..............Ans1
Add AB on both sides
PB+AB=PD+AB
PB+AB=PD+CD........AB=CD
PA=PC...........Ans2

Answered by Arun | 1st Feb, 2019, 11:46: AM