FINDING THE UNKNOWN IN TRIANGLE CIRCUMSCRIBING CIRCLE

Use Pythagoras' theorem in the following.

(Answer correct to 1 decimal place)

Problem 1 :

OM ⊥ AB. AO = 5 cm, OM = 4 cm. Find the length of AM and AB.

Solution:

By using Pythagorean Theorem,

OA² = OM² + AM²

5² = 4² + AM²

25 = 16 + AM²

AM² = 25 - 16

AM² = 9

AM = 3 cm

AB = 2 × AM

= 2 × 3

AB = 6 cm

So, length of chord AB is 6 cm.

Problem 2 :

OM ⊥ CD. MO = 6 m, OD = 8 m. Find the length of MD and CD.

Solution:

By using Pythagorean Theorem,

OD² = OM² + MD²

8² = 6² + MD²

64 = 36 + MD²

MD² = 64 - 36

MD² = 28

MD = 5.3 m

CD = 2 × MD

= 2 × 5.3

CD = 10.6 m

So, the length of chord CD is 10.6 m.

Problem 3 :

OM ⊥ EF. OM = 12 mm, OF = 13 mm. Find the length of FM and FE.

Solution:

By using Pythagorean Theorem,

OF² = OM² + FM²

13² = 12² + FM²

169 = 144 + FM²

FM² = 169 - 144

FM² = 25

FM = 5 mm

FE = 2 × FM

= 2 × 5

FE = 10 mm

Length of FM is 5 mm and length of FE is 10 mm.

Problem 4 :

OM ⊥ GH. MH = 8 cm, OM = 6 cm. Find the length of OH and GH.

Solution:

By using Pythagorean Theorem,

OH² = OM² + MH²

OH² = 6² + 8²

OH² = 36 + 64

OH² = 100

OH = √100

OH = 10 cm

GH = 2 × MH

= 2 × 8

GH = 16 cm

So, length of OH is 10 cm and GH is 16 cm.

Problem 5 :

OM ⊥ JK. KJ = 14 cm, OM = 3 m. Find the length of KM and OK.

Solution:

KJ = 14 cm = 0.14 m

By using Pythagorean Theorem,

OK² = OM² + KM²

OK² = 3² + (0.07)²

OK² = 9 + 0.0049

= 9.0049

OK = √9.0049

OK = 3 m

KM = 0.07 m

So, length of KM is 0.07 m and OK is 3 m.

Problem 6 :

OM ⊥ LP. OL = 10 m, LP = 18 mm. Find the length of LM and OM.

Solution:

LP = 18 mm = 0.018 m

By using Pythagorean Theorem,

OL² = OM² + LM²

10² = OM² + (0.0019)²

100 = OM² + 0.000081

OM² = 99.9

OM = √99.9

OM = 9.9 m

LM = 0.0019 m