O is the centre of the circle shown below. Line DHG is a tangent to the circle. Work out the size of angle a. Justify your answer.

Emu asked Nov 9, 2023

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30 votes

O is the centre of the circle shown below.

Line DHG is a tangent to the circle.

Work out the size of angle a. Justify your answer.

Emu asked Nov 9, 2023

by Emu

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23 votes

$\angle EHF=90^(\circ)$ (an angle inscribed in a semicircle is a right angle)

$\angle HEF=38^(\circ)$ (alternate segment theorem)

$a=52^(\circ)$ (angles in a triangle add to 180 degrees)

Kingston Chan answered Nov 15, 2023

2.8k points

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