Name: Chords of a Circle
Uploaded: 2019-07-19
Duration: 2 min 11 s
Description: A secant line to a circle is a line that crosses exactly two points on the circle, while a chord is a line that has its two endpoints on the circle. Watch th...

Question

Draw three triangles with lengths of two sides

4 cm

and

5 cm

and angle between them

60 °, 90 °

and

120 °

. Draw the circumcircle of each. (Note how the position of the circumcentre changes).

Accepted Answer

We know that, a circle, passing through all three vertices of a triangle is called the circumcircle of the triangle.

We can draw the circumcircle of any triangle by choosing as centre, the point of intersection of the perpendicular bisectors of two sides known as circumcentre of the circle.

Draw a line of length $4 cm$ .

By using protractor construct given angle $(60 °, 90 °, 120 °)$ from one end of the line.

By using compass cut the line at $5 cm$ , to get other line.

Join the two points to get the third side of the triangle.

Construct the perpendicular bisectors of the lines $4 cm, 5 cm$ , by taking radius more than half of the length and end of the line as centre.

The intersection point of perpendiculars gives the circumcentre.

By using compass, taking $o$ as centre and the perpendicular distance of the line as radius draw a circle.

Thus, the circle, which contains all three points of the triangle on them is the circumcircle.

In this triangle all the angles are less than $90 °$ . The circumcentre ‘ $O$ ’ is inside the triangle.

In the triangle with one angle is $90 °$ . The circumcentre is the midpoint of the hypotenuse.

In this triangle with an angle greater than $90 °$ . The circumcentre ‘ $O$ ’ is outside the triangle.

Kerala Board Solutions for Chapter: Circles, Exercise 4: Exercise 4

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Circles, Exercise 4: Exercise 4

Questions from Kerala Board Solutions for Chapter: Circles, Exercise 4: Exercise 4 with Hints & Solutions

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