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Geometry Level pending

E E is a point on the side A D AD of rectangle A B C D ABCD . So that D E = 6 DE=6 . Also D A = 8 DA=8 ; D C = 6 DC=6 . If C E CE extended meets the circumcirle of the rectangle at F F . find the length of D F DF .

Answer up to 3 decimal places.


The answer is 7.071.

Aswin T.S. by Aswin T.S. , 20, India

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1 solution

國聰 蕭
Mar 20, 2016

∠ D C F = 45 ° \angle DCF =45°

∠ D A F = ∠ D C F = 45 ° \angle DAF = \angle DCF =45°

B D 2 = 6 2 + 8 2 BD^2 = 6^2 + 8^2

B D = 10 BD = 10

sin ⁡ 45 ° D F = sin ⁡ 90 ° 10 \frac {\sin 45°}{DF} = \frac {\sin 90°}{10}

D F = 10 sin ⁡ 45 ° DF = 10 \sin 45°

D F = 7.071 DF = 7.071

(Sorry for no reason given)

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