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Tangents to Circles Worksheet



Drawback 1 :

Inform which line or phase is greatest described as a tangent within the diagram proven beneath. 

Drawback 2 :

Within the diagram proven beneath, inform whether or not the widespread tangents are inner or exterior. 

Drawback 3 :

Within the diagram proven beneath, inform whether or not the widespread tangents are inner or exterior.  

Drawback 4 :

Within the diagram proven beneath, describe all widespread tangent and establish the purpose of tangency. 

Drawback 5 :

Within the diagram proven beneath, say whether or not EF is tangent to the circle with heart at D.

Drawback 6 :

Within the diagram proven beneath, I’m standing at C, 8 ft from a grain silo. The gap from me to a degree of tangency is 16 ft. What’s the radius of the silo ? 

Drawback 7 :

Within the diagram proven beneath, 

SR is tangent at R to the circle with heart P

ST is tangent at T to the circle with heart P

Show : SR  ≅  ST

Drawback 8 :

Within the diagram proven beneath, 

AB is tangent at B to the circle with heart at C

AD is tangent at D to the circle with heart at C

Discover the worth of x.

Solutions

Drawback 1 :

Inform which line or phase is greatest described as a tangent within the diagram proven beneath.   

Reply :

EG is a tangent, as a result of it intersects the circle in a single level. 

Drawback 2 :

Within the diagram proven beneath, inform whether or not the widespread tangents are inner or exterior.  

Reply :

The traces j and okay intersect CD, they’re widespread inner tangents. 

Drawback 3 :

Within the diagram proven beneath, inform whether or not the widespread tangents are inner or exterior.  

Reply :

The traces m and n don’t intersect AB, so they’re widespread exterior tangents. 

Drawback 4 : 

Within the diagram proven beneath, describe all widespread tangent and establish the purpose of tangency. 

Reply :

The vertical line x  =  8 is the one widespread tangent of the 2 circles. 

The purpose of tangency is (8, 4). 

Observe : 

The purpose at which a tangent line intersects the circle to which it’s tangent is the purpose of tangency. 

Drawback 5 : 

Within the diagram proven beneath, say whether or not EF is tangent to the circle with heart at D.  

Reply :

We will use the Converse of the Pythagorean Theorem to say whether or not EF is tangent to circle with heart at D.  

As a result of 112 + 602  =  612, ΔDEF is a proper triangle and DE is perpendicular to EF.

So by Theorem 2, EF is tangent to the circle with heart at D.  

Drawback 6 :

Within the diagram proven beneath, I’m standing at C, 8 ft from a grain silo. The gap from me to a degree of tangency is 16 ft. What’s the radius of the silo ?    

Reply :

By the Theorem 1,  tangent BC is perpendicular to radius AB at B. So ΔABC is a proper triangle. So we are able to use the Pythagorean theorem.  

Pythagorean Theorem :

(r + 8)2  =  r2 + 162

Sq. of binomial :

r2 + 16r + 64  =  r2 + 256

Subtract r2 from both sides : 

16r + 64  =  256

Subtract 64 from both sides : 

16r  =  192

Divide both sides by 16. 

r  =  12

Therefore, the radius of the silo is 12 ft. 

Drawback 7 : 

Within the diagram proven beneath, 

SR is tangent at R to the circle with heart P

ST is tangent at T to the circle with heart P

Show : SR  ≅  ST

Reply :

Drawback 8 :

Within the diagram proven beneath, 

AB is tangent at B to the circle with heart at C

AD is tangent at D to the circle with heart at C

Discover the worth of x. 

Reply :

By the Theorem 3, two tangent segments from the identical level are congruent.

AB  =  AD

Substitute : 

x2 + 2  =  11

Subtract 2 from both sides. 

x2  =  9

Take sq. root on both sides. 

x  =  ± 3

Therefore, the worth of x is 3 or -3.

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