Ratio of Inscribed Circle Radii Equals the Similarity Ratio

Ratio of Inscribed Circle Radii Equals the Similarity Ratio. Practice questions to deepen understanding of the ratio of inscribed circle radii being equal to the similarity ratio. Online math practice with full solutions and step-by-step explanations.

Inscribed circle radii ratio practice — the ratio of inscribed circle radii equals the similarity ratio between similar triangles. Detailed explanations.

The ratio of inscribed circle radii equals the similarity ratio.

25 questions

Question 1

4.00 pts

📐 theorem similar triangles:
similar triangles ratio :

equal similarity ratio

equal square similarity ratio

area No

equal similarity ratio

Explanation:

:

two similar triangles, ratio equal ratio sides corresponding , similarity ratio .

:

three sides . . , sides , ratio:

side .
perimeter .
.

Yes similarity ratio small large/greater k, ratio small large/greater k. theorem calculate .

Question 2

4.00 pts

similarity ratio two similar triangles (smaller : larger) 2 5.
ratio (smaller : larger)?

2:5

4:25

5:2

1:1

Explanation:

, . similar triangles ratio :

sides ratio 2 5.
altitudes ratio 2 5.
ratio 2 5.

area square similarity ratio. Yes ratio 2 5.

Question 3

4.00 pts

two similar triangles. similarity ratio smaller : larger 3 4.
small 6 metres.

larger?

Explanation:

ratio small large/greater 3 4. small 6 3:

6 3 equal 2.
2 double 4 equal 8.

Yes large/greater 8 metres.

Question 4

4.00 pts

similarity ratio two similar triangles (smaller : larger) 2 7.
larger 21 metres.

small?

Explanation:

ratio small large/greater 2 7. large/greater small:

21 7 equal 3.
3 double 2 equal 6.

Yes small 6 metres.

Question 5

4.00 pts

: "ratio of areas similar triangles square similarity ratio, Yes ratio square similarity ratio".
?

area

Other

equal

similar triangles area

Explanation:

Correct ratio of areas similar triangles square similarity ratio, Correct area. , side altitude. ratio , No square .

Yes similarity ratio 2 3:

ratio 2 3.
ratio of areas 4 9.

Question 6

4.00 pts

Two similar triangles are shown. Inside each triangle, its inscribed circle is drawn.

similarity ratio smaller : larger 1 2, ratio ?

1 to 2

1 to 4

2 to 1

Always 1 to 1 because it is a circle.

Explanation:

Explanation: See the definition and relevant formula above.

Question 7

4.00 pts

small 3 metres.
larger 12 metres.

similarity ratio smaller : larger?

1:4

4:1

3:12

1:16

Explanation:

ratio small large/greater 3 12, 1 4. by/according to theorem exactly similarity ratio .

Question 8

4.00 pts

small similarity ratio ( ) 1 10.
0 8 metres.

0 8

0 08

Explanation:

ratio 1 10. large/greater 10 .

0 8 metres, Yes 0 8 double 10 equal 8.

8 metres.

Question 9

4.00 pts

similarity ratio two similar triangles (smaller : larger) 3 5.
larger 20 metres.
small : 20 double 5 3.

ratio ;

calculate

ratio

area No

Explanation:

because large/greater small, ratio small large/greater 3 5. small small large/greater:

small large/greater equal 3 5.

Yes small equal 20 double 3 5, No 20 double 5 3.

Question 10

4.00 pts

two similar triangles, one small one larger, two .

ratio 1 2, similarity ratio ?

1:2

1:4

2:1

4:1

Explanation:

Explanation: See the definition and relevant formula above.

Question 11

4.00 pts

metres ratio ?

equal three sides, Yes side

because No Yes No

area sides

metres

Explanation:

equal three sides. . , Yes k, k. Yes exactly side .

Question 12

4.00 pts

one 4 metres, two 9 metres.
ratio ratio two ?

Yes, similarity ratio small large/greater 4 9

No, because ratio always

Yes, angle

No, because by/according to

Explanation:

similarity ratio 4 9. one two 9 4, ratio. Yes ratio 4 9 ratio .

Question 13

4.00 pts

side k . r.
No ?

k double r

k square double r

r k

r square

Explanation:

sides . k:

side k.
sides k.

Yes k double r.

Question 14

4.00 pts

ratio smaller : larger 2 3.
ratio of areas smaller : larger?

4:9

2:3

3:2

1:1

Explanation:

ratio 2 3 ratio sides similarity ratio. ratio of areas similar triangles square similarity ratio:

2 square 3 square equal 4 9.

Yes ratio of areas small large/greater 4 9.

Question 15

4.00 pts

two one 5 metres.
necessarily similar triangles?

No, equal

Yes, equal necessarily

Yes, perimeters equal

Yes, because sides

Explanation:

one . , :

equilateral triangle.
right triangle .

Yes , No ratio identical similarity ratio.

Question 16

4.00 pts

A triangle and its inscribed circle are shown. The radius is marked in red from the center to one of the sides.

k ?

It is multiplied by k because it is a linear length in the triangle.

It is multiplied by k² as happens with area.

It stays constant because the circle is not affected.

It is multiplied by √k.

Explanation:

Explanation: See the definition and relevant formula above.

Question 17

4.00 pts

smaller : larger. small 2 metres, larger 6 metres.

ratio of areas smaller : larger?

1:9

1:3

3:1

2:6

Explanation:

ratio small large/greater 2 6, 1 3. similarity ratio. ratio of areas square similarity ratio:

1 square 3 square equal 1 9.

Yes ratio of areas small large/greater 1 9.

Question 18

4.00 pts

small larger . larger 22 metres, similarity ratio smaller : larger 4 9.

small?

Explanation:

ratio small large/greater 4 9. :

small large/greater equal 4 9.

small equal 22 double 4 9.

22 9 equal approx. 2 , double 4 10.

Yes small 10 metres.

Question 19

4.00 pts

two similar triangles equal.
?

similarity ratio 1 1 Yes

similarity ratio equal area

they are similar but cannot be congruent

Other

Explanation:

similar triangles equal, ratio 1 1. by/according to theorem similarity ratio, ratio sides 1 1. equal , .

Question 20

4.00 pts

known two because one ratio 2 5.
similar triangles?

No, ratio ; sides angles

Yes, ratio 2 5

Yes, one right-angled

Yes, area equal

Explanation:

side one , ratio . two ratio .

theorem sides known similar triangles. No .

Question 21

4.00 pts

, three .

small 6 larger 9, similarity ratio smaller : larger?

2:3

1:2

3:2

1:3

Explanation:

Explanation: See the definition and relevant formula above.

Question 22

4.00 pts

two similar triangles. ratio sides smaller : larger 5 6.
small 2 half metres.

larger?

2 half

Explanation:

similarity ratio small large/greater 5 6. Yes sides:

2 5 equal 0 5.
0 5 double 6 equal 3.

Yes large/greater 3 metres.

Question 23

4.00 pts

small larger . ratio smaller : larger 4 7.

ratio perimeters smaller : larger?

4:7

16:49

7:4

1:1

Explanation:

Yes ratio equal similarity ratio. perimeter sides Yes .

Yes ratio perimeters small large/greater 4 7.

Question 24

4.00 pts

. similar triangles. 1 2 metres, 6 metres.

similarity ratio ?

1:20

1:10

1:2

1:200

Explanation:

two No :

: 1 2 metres equal 120 metres.
: 6 metres.

ratio 6 120, 1 20. similarity ratio.

Question 25

4.00 pts

theorem similar triangles?

Yes similarity ratio exactly sides

area Yes No sides

angle ratio equal similarity ratio

ratio always square similarity ratio

Explanation:

theorem : two similar triangles, , , small by/according to ratio . one two k, :

side k.
perimeter k.
k.

area by/according to k square. large/greater area.