CBSE Class 9 Answered
Two equal chords AB and CD of a circle when
produced, intersect at point P. Prove that PB = PD.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
Expert Answer
Const: Join centre O to P. Draw Proof: We have,
AB = CD (given)
OR = OS (equal chords are equidistant from the centre)
In ORP and OSP,
OR = OS
(each 900)
and, OP = OP (common)
ORP OSP (RHS criterion)
RP = SP …..(i)
Now, AB = CD
BR = DS ……(ii)
Subtracting (ii) from (i)
RP - BR = SP - DS
PB = PD
Answered by | 04 Jun, 2014, 03:23: PM
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