Question 12 Marks
Draw different triangles of different measures and draw in circles and circumcircles of them. Complete the table of observations and discuss.
Questions
True False With Reason
Take a timed test
5 questions · self-marked practice — reveal the answer and mark yourself.
View full question & answer→
Question 22 Marks
Measure the lengths of the perpendiculars on chords in the following figures.
Did you find OL = OM in fig (i), PN = PT in fig (ii) and MA = MB in fig (iii)?
Write the property which you have noticed from this activity.
Answer
View full question & answer→In each figure, the chords are equidistant from the centre. Also, we can see that the measures of the chords in each circle are equal.
Thus, we can conclude that chords of a circle equidistant from the centre of a circle are congruent.
Thus, we can conclude that chords of a circle equidistant from the centre of a circle are congruent.
Question 32 Marks
Draw circles of convenient radii. Draw two equal chords in each circle. Draw perpendicular to each chord from the centre. Measure the distance of each chord from the centre. What do you observe?
Answer
View full question & answer→Congruent chords of a circle are equidistant from the centre.
Question 42 Marks
Every student from the group should do this activity. Draw a circle in your notebook. Draw a chord of the circle. Join the midpoint of the chord and centre of the circle. Measure the angles made by the segment with the chord.
Discuss about the measures of the angles with your friends. Which property do the observations suggest ?
Discuss about the measures of the angles with your friends. Which property do the observations suggest ?
Answer
View full question & answer→The meausure of the angles made by the drawn segment with the chord is 90°. Thus, we can conclude that, the segment joining the centre of a circle and the midpoint of its chord is perpendicular to the chord.
Question 52 Marks
Every student in the group should do this activity. Draw a circle in your notebook. Draw any chord of that circle. Draw perpendicular to the chord through the centre of the circle. Measure the lengths of the two parts of the chord. Group leader should prepare a table as shown below and ask other students to write their observations in it. Write the property which you have observed.
Answer
View full question & answer→On completing the above table, you will observe that the perpendicular drawn from the centre of a circle on its chord bisects the chord.