if O is the point of intersection of two chords AB and CD such that OB=OD and angle AOC=45 than triangles OAC and ODB ARE

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Q. In the figure,

O

is the point of intersection of two chords

A B

and

C D

such that

O B = O D

, then triangles

O A C

and

O D B

are:

Q. 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

Q. AB and CD are two chords of the circle with center O, which intersects at E.Prove that:

∠ A O C + ∠ D O B = 2 ∠ A E C

Q. In the given figure, two chords

A B

and

C D

of a circle intersect each other at a point

E

such that

∠

B A C = 45^{o}

∠

B E D = 120^{o}

. Then

∠

A B D =

Diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD.If AB = CD, then show that:
(i) ar ( $△$ DOC) = ar ( $△$ AOB) (ii) ar ( $△$ DCB) = ar ( $△$ ACB) [4 MARKS]

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