UKMT Special (Problem $21$ )

The diagram shows a circle and a trapezium $ABCD$ in which $AD$ is parallel to $BC$ and $AB = DC$ .

All four sides of $ABCD$ are tangents of the circle.

The circle has radius $4$ and the area of $ABCD$ is $72$ .

What is the length of $AB$ ?

[UKMT Hamilton Olympiad $2018$ , H $4$ ]

#Geometry

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Comments

Key point to realize is that the tangents to a circle from the same point will be of equal length.

Ethan Mandelez - 6 months, 3 weeks ago

Correct method and solution!

Yajat Shamji - 6 months, 2 weeks ago

You have until next Saturday, $3:00$ pm!

Yajat Shamji - 6 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

UKMT Special (Problem 212121)

Comments

UKMT Special (Problem $21$ )