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

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

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The area of an equilateral triangle with side length 6 cm is:

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What is the sum of the first 10 positive even numbers?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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How many diagonals does a pentagon have?

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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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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