This one is confusing! Please help

Q. There are 2 circles. 1 circle has its center as (0,5) and radius = 5 units. The other circle has its center as (12,0) and radius =12 units. A third circle is drawn which will pass through the center of the second circle and the two points of intersection of the other two circles. Find the radius of such a circle.

#Geometry #CoordinateGeometry #Circles

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

The equation of the first circle is $x^2 + (y-5)^2 = 25$

The equation of the second circle is $(x-12)^2 + y^2 = 144$

Solving them together, we get the two points of intersection of both the circles as $(0,0)$ and $\left( \dfrac{600}{169}, \dfrac{1440}{169} \right)$ .

Centre of the second circle is $(0,5)$

So the centre of the third circle ( say $(h,k)$ ) must be equidistant from the three points $(0,0)\ ; \left( \dfrac{600}{169}, \dfrac{1440}{169} \right) \ ; (0,5)$

Using distance formula, find the value of $h$ and $k$ . Radius of the circle would be the $\sqrt{h^2 + k^2}$ .

Do it yourself : Finding the values of $h,k$

Satyajit Mohanty - 5 years, 9 months ago

@Calvin Lin @Chew-Seong Cheong @Satyajit Mohanty @Pi Han Goh @Nihar Mahajan and all others.pPlease help

Anik Mandal - 5 years, 9 months ago

Is Answer 6 units

Hardik Gupta - 5 years, 9 months ago

How? pls explain

Pramita Kastha - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$