What must be the length of ZY in order for ZY to be tangent to circle X at point Y?
1 answer:
<h2>Explanation:</h2>
Hello! Remember you have to write complete questions in order to get good and exact answers. I'll assume that you have a circle X having two tangent lines that intersect at a point outside the circle. From geometry, we know that from any point outside a circle, two tangents to that circle are always congruent to each other if they meet at the mentioned point. So if the point of intersection is called Z, and a line is tangent to the circle at a point Y, ZY must be equal to ZW because ZW is tangent to the same circle at point W and meets ZY at a point outside the circle, then it is true that:
So <em>the ZY must be equal 3 in order for ZY to be tangent to circle X at point Y</em>
You might be interested in
Euclid's fifth postulate states, rather wordily, that:
<em>if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, </em><span><em>the two straight lines, if produced indefinitely, meet on that side </em><em>on</em><em> which are the angles less than the two right angles.
</em></span>
<em />If that sounds like a mouthful to you, you're not alone. Geometers throughout history found that postulate incredibly awkwardly-worded compared with his other four, and many in the 19th century rejected it outright and created a number of interesting new geometries from its ashes.
Euclid's fifth, put another way, states that two lines that aren't parallel will eventually meet, which consequently implies that <em>two parallel lines will never meet</em>. Without intending it, this property defines the space of Euclid's geometry to be <em>an infinite flat plane</em>.
If we take that parallel postulate and throw it out<em>, </em>then we've defined a <em>spherical space</em> for our geometry. Now, it doesn't matter where we draw our lines; <em>all of them will meet at some point</em>. If you need any convincing of this, take a look at the attached image. The longitude lines <em>seem </em>parallel at first, but they all eventually meet at the north and south poles.
<em>if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, </em><span><em>the two straight lines, if produced indefinitely, meet on that side </em><em>on</em><em> which are the angles less than the two right angles.
</em></span>
<em />If that sounds like a mouthful to you, you're not alone. Geometers throughout history found that postulate incredibly awkwardly-worded compared with his other four, and many in the 19th century rejected it outright and created a number of interesting new geometries from its ashes.
Euclid's fifth, put another way, states that two lines that aren't parallel will eventually meet, which consequently implies that <em>two parallel lines will never meet</em>. Without intending it, this property defines the space of Euclid's geometry to be <em>an infinite flat plane</em>.
If we take that parallel postulate and throw it out<em>, </em>then we've defined a <em>spherical space</em> for our geometry. Now, it doesn't matter where we draw our lines; <em>all of them will meet at some point</em>. If you need any convincing of this, take a look at the attached image. The longitude lines <em>seem </em>parallel at first, but they all eventually meet at the north and south poles.