Question

Activity I : Every student in the group will 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 will prepare a table and other students will write their observations in it. Fig. 6.3 

Answer 1

Student	1	2	3	4	5	6
l(AP)	2 cm	9 cm	12 cm	10 cm	10 cm	5 cm
l(PB)	2 cm	9 cm	12 cm	10 cm	10 cm	10 cm

Let us write the proof of this property.

Theorem: A perpendicular drawn from the centre of a circle on its chord bisects the chord.

Given: seg AB is a chord of a circle with centre O.

seg OP \(\perp\) chord AB

To prove: seg AP \(\cong\) seg BP

Proof: Draw seg OA and seg OB

In \(\triangle\)OPA and \(\triangle\)OPB

\(\angle\)OPA \(\cong\) \(\angle\)OPB ............. seg OP \(\perp\) chord AB

seg OP \(\cong\) seg OP .............common side

hypotenuse OA \(\cong\) hypotenuse OB ............ radii of the same circle

\(\therefore\) \(\triangle\)OPA \(\cong\) \(\triangle\)OPB  ........... hypotenuse side theorem

seg PA \(\cong\) seg PB ........... c.s.c.t.