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Angles In A Circle And Cyclic Quadrilateral — Flashcards

NIOS · Class 10 · Maths

28 flashcards for Angles In A Circle And Cyclic Quadrilateral (NIOS Class 10 Maths) to test yourself on key terms and facts.

41 questions28 flashcards8 formulas & key relations5 concepts

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A diagram illustrating the definitions of central angle and inscribed angle, showing an arc, the center of the circle, and a point on the remaining part of the circle.
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28 Flashcards·
Central angle and inscribed angleMinor arc and major arcArc length formulaArc length calculationAngle in a semicircleAngles in the same segment
Card 1Central angle and inscribed angle

Solve: In a circle, the central angle subtended by an arc is 70°. Find the inscribed angle subtended by the same arc.

Answer

Step 1: Use the relation central angle = 2 × inscribed angle. Step 2: Let the inscribed angle be x. Step 3: 70° = 2x Step 4: x = 70°/2 = 35° Answer: The inscribed angle is 35°.

Card 2Central angle and inscribed angle

Solve: The inscribed angle subtended by an arc is 28°. Find the central angle subtended by the same arc.

Answer

Step 1: Use central angle = 2 × inscribed angle. Step 2: Central angle = 2 × 28° Step 3: Central angle = 56° Answer: The central angle is 56°.

Card 3Minor arc and major arc

Solve: A minor arc has degree measure 125°. Find the degree measure of its corresponding major arc.

Answer

Step 1: Degree measure of major arc = 360° minus degree measure of corresponding minor arc. Step 2: Major arc = 360° - 125° Step 3: Major arc = 235° Answer: The major arc measures 235°.

Card 4Arc length formula

When do you use the formula Length of an arc = circumference × (degree measure of the arc)/360°? Show one example.

Answer

Use this formula when the arc measure and radius are known and the length of only part of the circle is needed. Example: If an arc measures 40° and the radius is r, then Length of arc = 2πr × 40°/360°…

Card 5Arc length calculation

Solve: A circle has radius 9 cm. Find the length of an arc whose degree measure is 80°.

Answer

Step 1: Use Length of an arc = circumference × degree measure/360°. Step 2: Circumference = 2πr = 2π × 9 = 18π cm. Step 3: Arc length = 18π × 80/360 Step 4: Arc length = 18π × 2/9 Step 5: Arc length =…

Card 6Angle in a semicircle

Why is the angle in a semicircle always a right angle?

Answer

Step 1: The angle at the centre subtended by a semicircle is 180°. Step 2: The central angle is double the inscribed angle. Step 3: So, 2 × inscribed angle = 180°. Step 4: Inscribed angle = 90°. Answe…

Card 7Angle in a semicircle

Solve: In a semicircle, an inscribed angle is formed at the circle. Find its measure.

Answer

Step 1: The angle subtended at the centre by a semicircle is 180°. Step 2: Central angle = 2 × inscribed angle. Step 3: 180° = 2x Step 4: x = 90° Answer: The angle is 90°.

Card 8Angles in the same segment

Solve: Two angles subtended by the same chord in the same segment are 42° and x°. Find x.

Answer

Step 1: Angles in the same segment of a circle are equal. Step 2: So the two angles must be equal. Step 3: x = 42° Answer: x = 42°.

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Frequently Asked Questions

What are the important topics in Angles In A Circle And Cyclic Quadrilateral for NIOS Class 10 Maths?
Key topics in Angles In A Circle And Cyclic Quadrilateral include Angles in a Circle, Concyclic Points and Cyclic Quadrilateral. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How many flashcards are available for Angles In A Circle And Cyclic Quadrilateral?
There are 28 flashcards for Angles In A Circle And Cyclic Quadrilateral covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Angles In A Circle And Cyclic Quadrilateral for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 41 practice questions on Angles In A Circle And Cyclic Quadrilateral. Revise definitions regularly and use flashcards for quick recall before the exam.

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