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In the given figure, O is the point of i...

In the given figure, O is the point of intersection of two chords AB and CD such that `OB=OD and angle AOC=45^(@)`. Then ,`Delta OAC and Delta ODB` are

A

equilateral and similar

B

equilateral but not similar

C

isosceles and similar

D

isosceles but not similar

Text Solution

Verified by Experts

The correct Answer is:
C
In `Delta OAC and Delta ODB`, we have
`angle AOC= angle DOB` ( ver. Opp. `angle`) and `angle OAC= angleODB` ( `angle` in the same segment)
`:. Delta OAC~ Delta ODB rarr (OC)/(OB)=(OA)/(OD)=(AC)/(BD)`
`:. (OC)/(OD) =1 rArr OC= OA [ :. OB =OD` (given)]
Clearly, `OAne OD`.
`:. (OA)/(OD) ne 1 rArr (AC)/(BD) ne rArr AC ne BD`
`:. Delta OAC and Delta ODB` are isosceles and similar.
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