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3 years ago

Please answer this multiple choice question!

Mathematics

2 answers:

Zina [86]3 years ago

7 0

Step-by-step Answer:

There is a theorem in geometry that states that a perpendicular (CQ) to any chord (PR) bisects the chord. This means that PQ=RQ=6cm.

koban [17]3 years ago

4 0

<h3>Answer: Choice B) 6 cm</h3>

==========================

Explanation:

Triangle PQC is congruent to triangle RQC. We can prove this through use of the hypotenuse leg theorem (HL theorem). Note that PC = RC are congruent radii, and also note that CQ = CQ through the reflexive theorem. We have a pair of hypotenuses and a pair of legs for the right triangles.

Then through CPCTC (corresponding parts of congruent triangles are congruent), we know that the pieces PQ and QR are congruent. For now, let's just call them x. They must add to PR which is 12, so,

PQ + QR = PR ..... segment addition postulate

x + x = 12

2x = 12

x = 6 ..... divide both sides by 2

QR = 6

This shows that if you have a radius perpendicular to a chord of a circle, then the radius will bisect this chord. Bisect means to cut in half.

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Step-by-step explanation:

I'm going to use $x$ instead of $\theta$ because it is less characters for me to type.

I'm going to start with the left hand side and see if I can turn it into the right hand side.

$\cot(x)+\cot(\frac{\pi}{2}-x)$

I'm going to use a cofunction identity for the 2nd term.

This is the identity: $\tan(x)=\cot(\frac{\pi}{2}-x)$ I'm going to use there.

$\cot(x)+\tan(x)$

I'm going to rewrite this in terms of $\sin(x)$ and $\cos(x)$ because I prefer to work in those terms. My objective here is to some how write this sum as a product.