Circle in a rectangle!

Geometry Level 5

A circle touches the sides A B AB and A D AD of a rectangle at P P and Q Q respectively and passes through the vertex C C . If the distance of C C from P Q PQ is 5 units. Then the area of the rectangle is:

Submit your answer as 2016 if you think there is insufficient information.


The answer is 25.

View wiki
Akhil Bansal by Akhil Bansal , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

The same problem had appeared a few moths back. There were two solutions, one was mine. I will comeback with a solution.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ahmad Saad
Jan 6, 2016

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How do you know that the angles marked X are equal ?

Des O Carroll - 5 years, 5 months ago

Log in to reply

The angle between a tangent and a chord meeting the tangent at the point of contact is equal to the inscribed angle on opposite side of the chord.

<PCQ = 45 , <BPC = <PQC Let, <PCB = X ---> <BPC = 90 - X ---> <PQC = 90 - X but, <PQC = 90 - <QCH ---> <QCH = X

Ahmad Saad - 5 years, 5 months ago

Log in to reply

Thanks Ahmed. I had forgotten about that theorem. I eventually solved the problem using coordinate geometry but your solution is far more elegant . good problem .

Des O Carroll - 5 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...