# Can anyone help me

$P,Q,R,S$ are the centres of the four circles each of which is cut by a fixed circle orthogonally. If $I^{2}_1,I^{2}_2,I^{2}_3,I^{2}_4$ are the squares of length of tangents to the four circles from a point in their plane then

$a.$ $I^{2}_1\Delta QRS-I^{2}_2\Delta RSP+I^{2}_3\Delta SPQ-I^{2}_4\Delta PQR=0$

$b.$ $I^{2}_1\Delta QRS+I^{2}_2\Delta RSP-I^{2}_3\Delta SPQ+I^{2}_4\Delta PQR=0$

$c.$ $I^{2}_1\Delta QRS-I^{2}_2\Delta RSP+I^{2}_3\Delta SPQ-I^{2}_4\Delta PQR=-1$

$d.$ none of these

Note by Anish Raj
3 years, 9 months ago

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.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 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"
MathAppears 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} $\boxed{123}$

Sort by:

@Nihar mahajan , @cheo-sheong cheong help

- 3 years, 9 months ago

Could you explain the notation that you have used in the first three options?

- 3 years, 9 months ago

Those are notation of “triange”.

- 3 years, 9 months ago

Even I know that.What I want to ask is what do we mean by $I1^2$triangle QRS.Does it mean square of tangent length from a fixed point to circumcircle of triangle QRS.

- 3 years, 9 months ago