Two circles C (O, r) and C (O', r') intersect at two points A and B and O lies on C(O', r'). A tangent CD is drawn to the circle C(O', r') at A. Then

∠ O A C = ∠ O A B

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∠ O A B = ∠ A O^{'} B

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∠ A O^{'} B = ∠ A O B

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∠ O A C = ∠ A O B

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Solution

The correct option is A $∠ O A C = ∠ O A B$
OB = OA (radius of circle)
$\Rightarrow ∠ C A O = ∠ O B A$
(angles in alternate segments are equal)
Now, if $∠ C A O = ∠ O B A$
$∴ ∠ O A C = ∠ O A B$
$S i n c e, ∠ O B A = ∠ O A B$ (Isosceles triangle)
$∴$ option (a) is correct

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Similar questions

Q. Two congruent circles with centres O and O' intersect at two points A and B. Then

∠ A O B = ∠ A O^{'} B

State True or False.

State true or false

Two congruent circles with centres O and O' intersect at two points A and B Then

∠ A O B = ∠ A O^{'} B

Q. Question 3
Write True or False and justify your answer :

The congruent circles with centres O and O' intersect at two points A and B. Then

∠ A O B = ∠ A O^{'} B

A, B, C

are three points on the circumference of a circle with centre

O

such that

∠ O A C = 53^{\circ}

and

∠ C B O = 32^{\circ}

, then

∠ A O B =

In the figure, AC is tangent to the circle at O and CB is is the perpendicular from C to O. If the radius of the circle is r, then, select the statement that is true.

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Two circles C (O, r) and C (O', r') intersect at two points A and B and O lies on C(O', r'). A tangent CD is drawn to the circle C(O', r') at A. Then

The correct option is A ∠OAC=∠OABOB = OA (radius of circle) ⇒∠CAO=∠OBA (angles in alternate segments are equal) Now, if ∠CAO=∠OBA ∴ ∠OAC=∠OAB Since,∠OBA=∠OAB (Isosceles triangle) ∴ option (a) is correct

The correct option is A $∠ O A C = ∠ O A B$
OB = OA (radius of circle)
$\Rightarrow ∠ C A O = ∠ O B A$
(angles in alternate segments are equal)
Now, if $∠ C A O = ∠ O B A$
$∴ ∠ O A C = ∠ O A B$
$S i n c e, ∠ O B A = ∠ O A B$ (Isosceles triangle)
$∴$ option (a) is correct