Let ABCD be a cyclic quadrilateral with sides AB = 2 cm, BC = 7 cm, CD = 11 cm, DA = 14 cm. Find the product of its diagonals.

125 cm

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120 cm

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364 cm

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34 cm

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Solution

The correct option is B 120 cm
Using Ptolemy's theorem,
$A C \times B D = (A B \times C D) + (A D \times B C)$
Substituting the values,
AC × BD = (2 × 11) + (14 × 7)
=120 cm

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Similar questions

A B C D

A B = 9 c m

B C = 6 c m

C D = 7 c m

A C = 9 c m

B D = 11 c m

Let ABCD be a quadrilateral with diagonals AC and BD. Prove the following statements (Compare these with the previous problem);

(a) AB + BC + CD > AD;

(b) AB + BC + CD + DA > 2AC;

(d) AB + BC + CD + DA > AC + BD.

A B C D, A B = 7 c m, B C = 6 c m, C D = 12 c m, D A = 15 c m, A C = 9 c m

90^{0}

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