Practice Brahmagupta's Formula For Cyclic Quadrilaterals (4.1.1.2.2.3) - Scientific and Technological
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Brahmagupta's Formula for Cyclic Quadrilaterals

Practice - Brahmagupta's Formula for Cyclic Quadrilaterals

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a cyclic quadrilateral?

💡 Hint: Think about the shape and its relation to a circle.

Question 2 Easy

What does Brahmagupta's formula calculate?

💡 Hint: Consider the measurements needed for area calculation.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the area of a cyclic quadrilateral?

A = (ab)
A = √[s(s−a)(s−b)(s−c)(s−d)]
A = (base × height) / 2

💡 Hint: Think of the formula that includes semi-perimeter.

Question 2

Brahmagupta's formula is applied only to which type of quadrilateral?

True
False

💡 Hint: Consider the definition of cyclic quadrilaterals.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

A cyclic quadrilateral has side lengths of 7, 9, 10, and 12. Prove that the area you calculate using Brahmagupta's formula is the same as if you divided it into triangles.

💡 Hint: Break down into triangles and apply their respective area formulas.

Challenge 2 Hard

Deduce why Brahmagupta's formula only applies to cyclic quadrilaterals, contrarily explain through inductive reasoning.

💡 Hint: Use inscribed angle property and relationships between angles and arcs.

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Reference links

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