(D) $(1)$ False. $A$ circle divides the plane on which it lies into three parts: the interior,the circle itself,and the exterior.$(2)$ False. If the d

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(D) $(1)$ False. $A$ circle divides the plane on which it lies into three parts: the interior,the circle itself,and the exterior.$(2)$ False. If the distance of a point from the centre of a circle is greater than its radius,the point lies in the exterior of the circle.

Class 9 Mathematics Circles Mix Examples - Circles

Easy

State whether each of the following statements is true or false:
$(1)$ $A$ circle divides the plane on which it lies into three parts.
$(2)$ $A$ point,whose distance from the centre of a circle is greater than its radius,lies in the interior of the circle.

A
True,True
B
True,False
C
False,True
D
False,False

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Mix Examples - Circles

$A, B$ and $C$ are three points on a circle. Prove that the perpendicular bisectors of $AB, BC$ and $CA$ are concurrent.

Difficult

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Prove that two circles cannot intersect at more than two points.

Easy

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$A$ circular park of radius $20\,m$ is situated in a colony. Three boys Ankur,Syed and David are sitting at equal distance on its boundary,each having a toy telephone in his hands to talk with each other. Find the length of the string of each phone.

Difficult

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Write True or False and justify your answer in each of the following:
If $A, B, C$ and $D$ are four points such that $\angle BAC = 45^{\circ}$ and $\angle BDC = 45^{\circ}$,then $A, B, C, D$ are concyclic.

Easy

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Write True or False and justify your answer in each of the following:
If $A, B, C, D$ are four points such that $\angle BAC = 30^{\circ}$ and $\angle BDC = 60^{\circ}$, then $D$ is the centre of the circle through $A, B$ and $C$.

Easy

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State whether each of the following statements is true or false:$(1)$ $A$ circle divides the plane on which it lies into three parts.$(2)$ $A$ point,whose distance from the centre of a circle is greater than its radius,lies in the interior of the circle.

Similar Questions

$A, B$ and $C$ are three points on a circle. Prove that the perpendicular bisectors of $AB, BC$ and $CA$ are concurrent.

Prove that two circles cannot intersect at more than two points.

$A$ circular park of radius $20\,m$ is situated in a colony. Three boys Ankur,Syed and David are sitting at equal distance on its boundary,each having a toy telephone in his hands to talk with each other. Find the length of the string of each phone.

Write True or False and justify your answer in each of the following:If $A, B, C$ and $D$ are four points such that $\angle BAC = 45^{\circ}$ and $\angle BDC = 45^{\circ}$,then $A, B, C, D$ are concyclic.

Write True or False and justify your answer in each of the following:If $A, B, C, D$ are four points such that $\angle BAC = 30^{\circ}$ and $\angle BDC = 60^{\circ}$, then $D$ is the centre of the circle through $A, B$ and $C$.

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State whether each of the following statements is true or false:
$(1)$ $A$ circle divides the plane on which it lies into three parts.
$(2)$ $A$ point,whose distance from the centre of a circle is greater than its radius,lies in the interior of the circle.

Write True or False and justify your answer in each of the following:
If $A, B, C$ and $D$ are four points such that $\angle BAC = 45^{\circ}$ and $\angle BDC = 45^{\circ}$,then $A, B, C, D$ are concyclic.

Write True or False and justify your answer in each of the following:
If $A, B, C, D$ are four points such that $\angle BAC = 30^{\circ}$ and $\angle BDC = 60^{\circ}$, then $D$ is the centre of the circle through $A, B$ and $C$.