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प्रश्न
In the given figure, AB is a side of a regular hexagon and AC is a side of a regular eight-sided polygon.
Find:
(i) ∠AOB
(ii) ∠AOC
(iii) ∠BOC
(iv) ∠OBC
उत्तर
As AB is the side of a hexagon so the
∠AOB = `(360°)/6` = 60°
AC is the side of an eight-sided polygon so,
∠AOC = `(360°)/8` = 45°
From the given figure we can see that:
∠BOC = ∠AOB + ∠AOC
⇒ 60° + 45° = 105°
Again, from the figure, we can see that ∠BOC is an isosceles triangle with sides BO = OC as they are the radii of the same circle.
Angles ∠OBC = ∠OCB as they are opposite angles to the equal sides of an isosceles triangle.
Sum of all the angles of a triangle is 180°
∠OBC + ∠OCB + ∠BOC = 180°
2∠OBC + 105° = 180° as, ∠OBC = ∠BOC
2∠OBC = 180° - 105°
2∠OBC = 75°
∠OBC = 37.5° = 37°30'
As, ∠OBC = ∠BOC
∠OBC = ∠BOC = 37.5° = 37°30'.
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संबंधित प्रश्न
In the figure given alongside, AB and CD are straight lines through the centre O of a circle. If ∠AOC = 80° and ∠CDE = 40°, find the number of degrees in:
- ∠DCE,
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Two chords AB and CD intersect at P inside the circle. Prove that the sum of the angles subtended by the arcs AC and BD at the centre O is equal to twice the angle APC.
The given figure shows a circle with centre O such that chord RS is parallel to chord QT, angle PRT = 20° and angle POQ = 100°. Calculate:
- angle QTR
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The given figure shows a circle with centre O such that chord RS is parallel to chord QT, angle PRT = 20° and angle POQ = 100°. Calculate:
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The given figure shows a circle with centre O such that chord RS is parallel to chord QT, angle PRT = 20° and angle POQ = 100°. Calculate:
(iii) angle QRS
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(iv) angle STR
In the given figure, O is the center of the circle and the length of arc AB is twice the length of arc BC. If ∠AOB = 100°,
find: (i) ∠BOC (ii) ∠OAC
In the given figure, a square is inscribed in a circle with center O. Find:
- ∠BOC
- ∠OCB
- ∠COD
- ∠BOD
Is BD a diameter of the circle?
In the given figure, AB = BC = DC and ∠AOB = 50°.
(i) ∠AOC
(ii) ∠AOD
(iii) ∠BOD
(iv) ∠OAC
(v) ∠ODA
C is a point on the minor arc AB of the circle, with centre O. Given ∠ACB = p°, ∠AOB = q°.
(i) Express q in terms of p.
(ii) Calculate p if ACBO is a parallelogram.
(iii) If ACBO is a parallelogram, then find the value of q + p.
