Advertisements
Advertisements
Question
If ABC is an arc of a circle and ∠ABC = 135°, then the ratio of arc \[\stackrel\frown{ABC}\] to the circumference is ______.
Options
1 : 4
3 : 4
3 : 8
1 : 2
Advertisements
Solution
If ABC is an arc of a circle and ∠ABC = 135°, then the ratio of arc \[\stackrel\frown{ABC}\] to the circumference is 1 : 4.
Explanation:
Given:
ABC is an arc.
∠ABC = 135°,
Calculation:
Let r be the radius of the circle.
Construction, take a point D in the alternative segment. Join AD to CD.
∠ABC + ∠ADC = 180° (opposite angles of a cyclic quadrilateral)
= 135° + ∠ADC = 180°
= ∠ADC = 180° − 135°
= ∠ADC = 45°
∠AOC = 2 × ADC
= ∠AOC = 2 × 45° = 90°
Hence, the arc ABC represent quadrant of the circle.
Length of arc ABC = `[1/4]` × 2πr
= Length of arc ABC = `[1/4]` × Circumference of the Circle
Length of arc ABC : Circumference of the circle
= 1 : 4
APPEARS IN
RELATED QUESTIONS
Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.
If O is the centre of the circle, find the value of x in the following figure
If O is the centre of the circle, find the value of x in the following figure
If O is the centre of the circle, find the value of x in the following figures.
Prove that the angle in a segment shorter than a semicircle is greater than a right angle.
In the given figure, two circles intersect at A and B. The centre of the smaller circle is Oand it lies on the circumference of the larger circle. If ∠APB = 70°, find ∠ACB.
In the given figure, two congruent circles with centres O and O' intersect at A and B. If ∠AOB = 50°, then find ∠APB.
In the given figure, A is the centre of the circle. ABCD is a parallelogram and CDE is a straight line. Find ∠BCD : ∠ABE.
In the given figure, if O is the circumcentre of ∠ABC, then find the value of ∠OBC + ∠BAC.
The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is
