Maths / Circles / Equal Chords of a Circle Subtend Equal Angle at the Centre

QUESTION

 In the given figure, O is the centre of the circle and AM = 4 units. $\angle AOM = 60^0$$\angle POQ = 60^0$ The perimeter of $\Delta POQ$ is

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{120} \fn_jvn \large In \Delta AOM\; \and\;\angle AOM = 60^0$

$\angle OAM =\angle OMA$ angle opposite equal sides are equal

$\angle OAM =\angle OMA = x$

$in \Delta AOM$

$x + x+ 60^0 = 180^0$

$2x = 120^0$

$x = 60^0$

$\Delta AOM\; is\; an\; equilateral\; triangle$

perimeter 0f $\Delta AOM$ =  4+ 4+ 4= 12 units

As equal chords subtend equal angle and $\angle POQ = 60^0$

PQ= AM = 4units

perimeter 0f $\Delta POQ$ =  4+ 4+ 4= 12 units

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