Math Is Fun Forum

apsara123

Member

Registered: 2016-05-14

Posts: 20

Problems

I need help with these problems:

1)Let $\triangle ABC$ be a right triangle such that $B$ is a right angle. A circle with diameter of $BC$ meets side $AC$ at $D.$ If the area of $\triangle ABC$ is $150$ and $AC = 25,$ then what is $BD$?

2)A decorative arrangement of floor tiles forms concentric circles, as shown in the figure to the right. The smallest circle has a radius of 2 feet, and each successive circle has a radius 2 feet longer. All the lines shown intersect at the center and form 12 congruent central angles. What is the area of the shaded region? Express your answer in terms of $\pi$.

Picture for number 2 is :

3) Let $ABC$ be a triangle. We construct squares $ABST$ and $ACUV$ with centers $O_1$ and $O_2$, respectively, as shown. Let $M$ be the midpoint of $\overline{BC}$.

(a) Prove that $\overline{BV}$ and $\overline{CT}$ are equal in length and perpendicular.

(b) Prove that $\overline{O_1 M}$ and $\overline{O_2 M}$ are equal in length and perpendicular.

Thank you so much!!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Problems

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Problems

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Problems

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

apsara123

Member

Registered: 2016-05-14

Posts: 20

Re: Problems

I still need help with part a and part b. I used congruent triangles to show that the lengths are equal in part a but I can't prove their perpendicular. And for part B I have absolutely no idea to start! Please help. thank you.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Problems

Hi apsara123

You are using $ symbol in your text . add math & /math tags within []and write text within  \text {} to get proper look.

Last edited by thickhead (2016-07-08 21:54:32)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

apsara123

Member

Registered: 2016-05-14

Posts: 20

Re: Problems

Thank you!!