Question

Question 2:
In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then
(1) What is the length of each tangent segment ?
(2) What is the measure of ∠MRO ?
(3) What is the measure of ∠ MRN ?​

Answer 1

Answer:

OMR=∠ONR=90

o

OM=5 cm OR=10cm

OR

2

=OM

2

+MR

2

MR=

OR

2

−OM

2

=

10

2

−5

2

=5

3

cm

(2) in right △OMR

tan∠MRO=

MR

OM

tan∠MRO=

5

3

cm

5 cm

=

3

1

(3) ∠MRO=30 o

∠MRN=∠MRO+∠NRO=30

o+30

o=60

∠MRN=60 o