Make Triangle

Geometry Level 3

PQRS is a rectangle with PQ=16 cm and QR=12 cm . If ABCD is a rhombus formed PQRS , what is the radius of the circle incribed in rhombus ABCD?


The answer is 4.8.

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2 solutions

We note that △ A B O \triangle ABO is Pythagorean ( 3 : 4 : 5 3:4:5 ). We also note that △ A T O \triangle ATO is similar to △ A B O \triangle ABO , therefore, O T O A = r 6 = 4 5 \dfrac{OT}{OA} = \dfrac{r}{6} = \dfrac{4}{5} ⇒ r = 4 × 6 5 = 4.8 \Rightarrow r = \dfrac{4\times 6}{5} = \boxed{4.8}

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Ramiel To-ong
Dec 15, 2015

good solution:

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