Two chords, KL and MN, of a circle intersect at an external
point J. If KL = 15 cm. LJ = 5 cm, MN = 21 cm and NJ = 4 cm,
find area(quadrilateral KLNM)
area(AJKM).
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Explanation:
Two chords KL and MN of a circle intersect at an external point J. If KL= 15 cm, L J =5cm, MN= 21 cm and NJ= 4 cm, then what will be the ratio of the area of the quadrilateral KLNM to the area of the triangle JKM?
Area of triangle JLN = {5*4*sin J}/2 = 10 sin J
Area of triangle JKM = {20*25*sin J}/2 = 250 sin J
Area of quadrilateral KLNM = Area of triangle JKM - Area of triangle JLN
= 250 sin J - 10 sin J
= 240 sin J
Ratio of of the area of the quadrilateral KLNM to the area of the triangle JKM = 240 sin J : 250 sin J
= 24 : 25.
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