Question

5

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by these points. 

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Answer 1

Step-by-step explanation:

answer to this question is 28 cm°2

Answer 2

Step-by-step explanation:

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SOLUTION:-

Construction: Draw perpendiculars OE and OF onto AE and CD respectively from the centre O.

In ΔOEB,OE

2+BE2 = OB2

[Using Pythagoras theorem]

OE

2 = OB2- BE2

OE2= 25 - 9

(Perpendicular drawn from centre to a chord bisects the chord, so BE = 3cm)

Therefore, OE = 4cm

Similarly In

ΔOFD,OF2+ FD2 = OD2

OF2 = OD2- FD2

OF2=25−16=9

(Perpendicular drawn from centre to a chord bisects the chord, so FD = 4 cm)

⇒ OF = 3 cm

Here, the figure formed by the points A, B, C and D is a quadrilateral with one pair of sides parallel to each other.

Hence, ABCD is a trapezium.

We have,

Area of trapezium = 1

2

(perpendicular distance between two parallel sides)(sum of the lengths of the parallel sides)

=12x (OE + OF) x (AB + CD)= 12(4+3)(8+6)

= 49 cm2.