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Simple and Easy Learning
Tutorials Point originated from the idea that there exists a class of readers who respond better to online content and prefer to learn new skills at their own pace from the comforts of their drawing rooms.
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Tutorialspoint
76 Views
Given:$\angle ABC = 69^o, \angle ACB = 31^o$To do:We have to find $\angle BDC$.Solution:We know that, Angles in the same segment of a circle are equal.This implies, $\angle BAC = \angle BDC$In $\triangle ABC$, $\angle ABC+\angle BAC+\angle ACB = 180^o$ (The sum of the angles of a triangle ... Read More
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Tutorialspoint
101 Views
Given: Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius \( 5 \mathrm{~m} \) drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. The distance between Reshma and Salma and between Salma and Mandip is \( ... Read More
Tutorialspoint
229 Views
Given:A circular park of radius \( 20 \mathrm{~m} \) is situated in a colony. Three boys Ankur, Syed and David are sitting at an equal distance on its boundary each having a toy telephone in his hands to talk to each other.To do:We have to find the length of the ... Read More
Tutorialspoint
97 Views
Given:Two circles intersect at two pointsTo do:We have to prove that their centres lie on the perpendicular bisector of the common chord.Solution:Let two circles with centres $O$ and $O'$ intersect each other at $A$ and $B$.$OA = OB$ (Radii of the circle)$O’A = ... Read More
Tutorialspoint
68 Views
Given:Radii of two circles are \( 5 \mathrm{~cm} \) and \( 3 \mathrm{~cm} \).The distance between the centre of the circles is \( 4 \mathrm{~cm} \).To do :We have to find the length of the common chord.Solution: In the above figure, $AO=5\ cm, BO=3\ cm$$AB = 4\ cm, AC = x, ... Read More
Tutorialspoint
128 Views
Given:Two equal chords of a circle intersect within the circleTo do:We have to prove that the segments of one chord are equal to corresponding segments of the other chord.Solution:Let $AB$ and $CD$ be two equal cords which intersect at point $R$.From the centre of the circle, draw a perpendicular to ... Read More
Tutorialspoint
89 Views
Given:Two equal chords of a circle intersect within the circleTo do:We have to prove that the line joining the point of intersection to the centre makes equal angles with the chords.Solution:Let $AB$ and $CD$ be two equal cords which intersect at point $R$.$PQ$ is the diameter of the circle.From the ... Read More
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Tutorialspoint
51 Views
Given:$A, B$ and $C$ are three points on a circle with centre $O$ such that $\angle BOC = 30^o$ and $\angle AOB = 60^o$.$D$ is a point on the circle other than the arc $ABC$.To do:We have to find $\angle ADC$.Solution:Draw a line segment from $O$ to $AD$ such that ... Read More
Tutorialspoint
45 Views
To do:We have to fill in the blanks. Solution:(i) The centre of a circle lies in interior of the circle.(ii) A point, whose distance from the centre of a circle is greater than its radius lies in the exterior of the circle.(iii) The longest chord of a circle is a diameter of the circle.(iv) An ... Read More
Tutorialspoint
90 Views
To do:We have to state whether the given statements are true or false.Solution:(i) We know that, A line segment joining the centre to any point on the circle is a radius of the circle.Therefore, The given statement is true. (ii) We know that, A circle has infinite number of equal chords.Therefore, ... Read More