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 :

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} = r^{2} + 16^{2}

Sq. of binomial :

r^{2} + 16r + 64 = r^{2} + 256

Subtract r^{2} 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 :

x^{2} + 2 = 11

Subtract 2 from both sides.

x^{2} = 9

Take sq. root on both sides.

x = ± 3

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

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