What is the permeter of square ABCD?

Mathematics

1 answer:

marshall27 [118]3 years ago

7 0

Answer:

24.3 units (3 s.f.)

Step-by-step explanation:

Since a square has 4 equal sides,

perimeter of ABCD= 4(length of AB)

Distance between 2 points

= $\sqrt{(y1 - y2)^{2} + (x1 - x2)^{2} }$

Length of AB

$= \sqrt{( { - 2 - 4)}^{2} + {(2 - 3)}^{2} } \\ = \sqrt{( - 6)^{2} + ( - 1)^{2} } \\ = \sqrt{37}$

perimeter of ABCD

$= 4 \sqrt{37} \\ = 24.3 \: units \: (3 \: s.f.)$

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Line segment TS is tangent to circle O at point N.

garik1379 [7]

Answer:

148°

Step-by-step explanation:

The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.

arc QN = 2(74°) = 148°

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<em>Comment on the question and answer</em>

Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.

We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.