Angles In A Circle And Cyclic Quadrilateral
NIOS · Class 10 · Maths
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Get startedSolve: 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°.
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°.
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°.
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°…
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 =…
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…
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°.
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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