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Circle O has a radius of 5 cm. The length of a chord AB is 8 cm. Circle Q is tangent to a chord and to the arc AB as well. (See diagram below) If line segment AM is 2 cm, what's the area of a circle Q? 

 

 Dec 26, 2020
 #1
avatar+112009 
+2

I haven't worked out how to do it with theoretical geometry and Algebra.

 

But here it is drawn to scale.

The radius is approx (maybe exact)  0.75

so the area is  approx  0.5625pi  cm^2

 

 Dec 27, 2020
 #2
avatar+836 
+3

I'll use your graph, if I may?!smiley 

 

Note that the y-axis is parallel to a chord AB, and the distance between them is 3 cm.

 

The coordinates of the points P and O are:     P (0, 2)       O (0, 0)        MD = ND ==>  r

 

PO = 2       PM = 3          ON = 5

 

PO2 + (PM + r)2 = (ON - r)2

 

22 + (3 + r)2 = (5 - r)2    ==>     r = 0.75

 

A = (3/4)2pi cm2

jugoslav  Dec 27, 2020
edited by jugoslav  Dec 27, 2020
 #3
avatar+112009 
+1

 

That is a neat answer Jugoslav.   laugh

Thanks, I was having a mental block.   blush

 

 

The only thing you forgot is that it has to be shown that AB has a perpendicular distance to (0,0) of 3 units.

This is not hard to do, you can just use the Pythagorean triad 3-4-5  but it does have to be shown before your part of the calculations.

Melody  Dec 27, 2020
edited by Melody  Dec 27, 2020

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