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 sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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What is the greatest common divisor (GCD) of 36 and 48?

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How many ways can 4 people sit in a row?

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What is the area of an equilateral triangle with side length 10 cm?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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