The diagonals of the cyclic quadrilateral $$\(A B C D\)$$ intersect at $$\(X\)$$. $$\(A D=10 \mathrm{~cm}, B C=8 \mathrm{~cm}, B X=5 \mathrm{~cm}\)$$ and $$\(C X=7 \mathrm{~cm}\)$$. (a) Calculate $$\(D X\)$$. $$\(D X=\)$$ ....................................... $$\(\mathrm{cm}\)$$ (b) Calculate angle $$\(B X C\)$$. Angle $$\(B X C=\)$$ ............................................
Exam No：0580_w20_qp_42 Year：2020 Question No：8(c)(ii)
Answer:
(a) \(8.75\) or \(83 / 4\)
(b) \(81.8\) or \(81.78\) to \(81.79\)
(b) \(81.8\) or \(81.78\) to \(81.79\)
Knowledge points:
E4.4.1 Calculate lengths of similar figures.
E4.4.2 Use the relationships between areas of similar triangles, with corresponding results for similar figures and extension to volumes and surface areas of similar solids.
E6.4 Solve problems using sine and cosine rules and the area formula for triangles.
Solution:
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