A geometry problem by Saurav Pal

Geometry Level 2

Find X in the above figure if the blue lines are concurrent.

62 17 \frac{62}{17} 56 18 \frac{56}{18} 64 17 \frac{64}{17} 56 15 \frac{56}{15}

Saurav Pal by Saurav Pal , 26, India

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2 solutions

Mahdi Raza
Jan 16, 2020

By Ceva's theorem x 2 ⋅ 3 7 ⋅ 5 4 = 1 \frac{x}{2}\cdot\frac{3}{7}\cdot\frac{5}{4} = 1 15 x 56 = 1 \frac{15x}{56} = 1 x = 56 15 \boxed{x = \frac{56}{15}}

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Shithil Islam
Jan 2, 2017

In a triangle ABC, the cevians are AP,BQ,CR and they are concurrent. So we can say that,

(BP CQ AR) / (PC QA RB) = 1

(3 5 x) / (2 7 4) = 1

15x / 56 = 1

So, x = 56/15

0 Helpful 0 Interesting 0 Brilliant 0 Confused

according to Ceva's theorem
(x/2)(3/7)(5/4)= 1 so 15x=56 x=56/15

geoff taylor - 3 years, 5 months ago

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