IGCSE Mathematics Paper-1: Specimen Questions with Answers 167 - 168 of 175

Question number: 167

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Short Answer Question▾

Write in Short

The area of a square is 42.25 . Find length of one side of the square.

Explanation

Here, formula for area of a square = where, a is side of square.

  • So, here,

Question number: 168

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Essay Question▾

Describe in Detail

In the diagram AC is the diameter of a circle, center O. The length of AC is 12 cm.

A circle having a triangle on half part

A Circle Having a Triangle on Half Part

Find the given calculations by using the appropriate formulas of circle and triangle

(a) Write down the size of angle ABC.

(b) Angle BAC = 40°. Calculate the length of BC.

(c) Calculate the area of the circle.

Explanation

Here, AC is the diameter of a circle which is of 12 cm and O is center.

(a) Size of

Here, edge AC of triangle is diameter of the circle which will be diagonal of triangle ABC.

So, we can see in the figure, it is a right angled triangle, so

  • The triangle formed by the diameter and the inscribed angle (triangle ABC above) is always a right triangle.

(b) Here, Angle BAC = 40° and length of AC is 12 cm.

So, using cosine formula of triangle:

(C) Area of circle = , where r = radius of circle.

So, here diameter AC = 12 cm, so radius = .

So, area of circle = .