Question

In the given figure, O is the point of intersection of two chords AB and CD such that OB = OD and ∠AOC = 45° . Then, ∆OAC and ∆ODB are 

(a) equilateral and similar 

(b) equilateral but not similar 

(c) isosceles and similar 

(d) isosceles but not similar

Answer 1

(c) isosceles and similar 

In ∆AOC and ∆ODB, we have: 

∠AOC = ∠DOB (Vertically opposite angle) 

and ∠OAC = ∠ODB (angle in the same segment) 

therefore,by AA similarity theorem, we conclude that  ∆AOC − ∆DOB.

⟹ OC = OA 

Hence, ∆OAC and ∆ODB are isosceles and similar