Circle
A 2-dimensional shape made by drawing a curve that is always the same distance from a centre.
Summary
A 2-dimensional shape made by drawing a curve that is always the same distance from a centre.
Things to Remember
A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre)
MCQs
No MCQs found.
Subjective Questions
Q1:
What is a state?
Type: Very_short Difficulty: Easy
Q2:
What are the elements of a state?
Type: Long Difficulty: Easy
<ul>
<li>Government</li>
<li>Population</li>
<li>Territory</li>
<li>Sovereignty</li>
</ul>
<ol>
<li><strong>Government<br /></strong>A government is the group of people that governs a community or unit. It is the system by which a state or community is controlled. It is an agency through which state formulates its plans and policies.</li>
<li><strong>Population</strong><br />The population is the primary element of the state. There is no hard and fast rule about population. There is no definite number of people required to be a state. But it should be large enough to be self-sufficient. The permanent population of the state is called citizens.</li>
<li><strong>Territory</strong><br />A definite and more or less permanent territory are also regarded as an essential element of the state. In modern times, the citizens are bound together by a residence on a common territory. Land, water, and airspace comprise the territory of a state.</li>
<li><strong>Sovereignty</strong><br />In a democratic country, people are considered having sovereign power. It is also the quality of having supreme, independent authority over the territory. Sovereignty has two aspects; internal and external. Internally viewed, the state has supreme power over all individuals and associations within its fixed area. Externally viewed, the state is free from the control of any foreign state or alien rule.</li>
</ol>
Q3:
How many people is required for the territory to be recognized as a state?
Type: Short Difficulty: Easy
Q4:
Why does a state need territory?
Type: Very_short Difficulty: Easy
Q5:
What role does government play?
Type: Short Difficulty: Easy
Q6:
Define sovereignty.
Type: Short Difficulty: Easy
Q7:
What do you mean by territory ?
Type: Very_short Difficulty: Easy
Q8:
Define population.
Type: Short Difficulty: Easy
Q9:
What do you mean by dictatorship?
Type: Short Difficulty: Easy
Q10:
Write all the four elements of a state?
Type: Short Difficulty: Easy
<ul>
<li>Population</li>
<li>Territory</li>
<li>Government</li>
<li>Sovereignty</li>
</ul>
Videos
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Territory
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Sovereignty
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Circle
Figures given below will show the different part of a circle.
Now, we study about the central angle, inscribed angle, cyclic quadrilateral, tangents and related theorems.
Central Angle
In the circle PQR, radii OP and OQ form an angle at the centre O. So, acute ∠POQ and reflex ∠POQ are central angles. The part PQ of the circle is an arc.
∠POQ is subtended by \(\widehat{PQ}\) and reflex∠POQ is subtended by \(\widehat{PRQ}\). As the length of arc increases, the measure of the central angle subtended by the arc also increases. So the central angle can be measured with its corresponding opposite arc. Therefore∠POQ =\(\widehat{PQ}\) and reflex∠POQ = \(\widehat{PRQ}\)
Angle at the circumference (Inscribed angle)
The angle formed by joining the two chords at the circumference of a circle is called angle at the circumference or inscribed angle. In the adjoining figure, chord AB and chord CB meet at the point B on the circumference and ∠POQ is formed which is angle at circumference standing on the arc AC \((\widehat {AC})\). Inscribed angle also can be measured (expressed) in terms of its corresponding arc \( [\angle ABC = \frac {1}{2} \widehat {AC}]\)
Arc formed by a chord
In a circle ABC, chord AB divides the circle into two parts. The arc AB \((\widehat {AB}\) is formed by the chord AB. In this way, while reading an arc and its corresponding chord, we use the same letter but the length is not exactly same. In the adjoining figure \(\widehat{AB}\) is a minor arc and \(\widehat{ACB}\) is major arc. In short \(\widehat{ADB}\) is read as minor\(\widehat{AB}\) and \(\widehat{ACB}\) is read as major\( \widehat{AB}\).
Cyclic quadrilateral
If all the vertices of a quadrilateral are on the circumference of a circle, then the quadrilateral is called cyclic quadrilateral. In the adjoining figure, ABCD is a cyclic quadrilateral. In other words, the quadrilateral inscribed in a circle is called cyclic quadrilateral. The points A, B, C, D are concyclic ABCD is cyclic quadrilateral but ABCE and ADCE are not cyclic quadrilaterals.
Lesson
Geometry
Subject
Compulsory Mathematics
Grade
Grade 10
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