Topic Details (Notes format)

How to Understand Circle Theorems (Angles and Tangents)

Subject: Mathematics

Book: Maths Mastery

Circle theorems unlock relationships like the angle at the center being twice the angle at the circumference, or the fact that tangents from a point outside the circle are equal in length. For instance, if an inscribed angle subtends an arc of 80°, the central angle subtending the same arc measures 160°. These insights help solve complex geometry problems, design circular arcs, or interpret arc-based data in advanced fields. Familiarizing yourself with circle theorems ensures you can tackle chord bisections, tangential segments, and cyclical quadrilaterals with precision.

Practice Questions

The probability of rolling a sum of 7 with two dice is:

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What is the cube root of 729?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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What is the sum of the interior angles of a hexagon?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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A car travels 240 km in 4 hours. What is its average speed?

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If a square has a perimeter of 64 cm, what is its area?

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What is the sum of all even numbers between 1 and 50?

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