Advertisements
Advertisements
Question
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
Solution
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'.
APPEARS IN
RELATED QUESTIONS
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,
- ∠ABC.
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.
In the given figure, AB = AC = CD and ∠ADC = 38°. Calculate :
- Angle ABC
- Angle BEC
In the given figure, ABC is a triangle in which ∠BAC = 30°. Show that BC is equal to the radius of the circumcircle of the triangle ABC, whose centre is O.
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
- angle QRP
- angle QRS
- angle STR
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
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, the lengths of arcs AB and BC are in the ratio 3:2. If ∠AOB = 96°, find:
- ∠BOC
- ∠ABC
In the given figure, AB is a side of regular pentagon and BC is a side of regular hexagon.
(i) ∠AOB
(ii) ∠BOC
(iii) ∠AOC
(iv) ∠OBA
(v) ∠OBC
(vi) ∠ABC
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.
