# NMTC Problem 2

$$ABCD$$ is a quadrilateral inscribed in a circle with centre $$O$$. Let $$BD$$ bisect $$OC$$ perpendicularly. $$P$$ is a point on $$AC$$ such that $$PC=OC$$. $$BP$$ cuts $$AD$$ at $$E$$ and the circle $$ABCD$$ at $$F$$. Prove that $$PF$$ is the geometric mean of $$EF$$ and $$BF$$.

This a part of my set NMTC 2nd Level (Junior) held in 2014.

Note by Siddharth G
3 years, 8 months ago

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} $$\boxed{123}$$