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

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. Kindly mail your suggestions to v4formath@gmail.com

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