Pls hlp me to sort it out this prmblm guys..
Answers
Answer(i):
x = 42°
Step-by-step explanation:
Given:-
- A circle with center O
- AB = 3 cm
- CD = 3 cm
- ∠COD = 42°
Solution:-
In ΔAOB and ΔCOD, we have
OA = OD, [Both equal to the radius of the circle]
OB = OC, and [Both equal to the radius of the circle]
AB = CD = 3 cm [Given]
So, by SSS-congruence criterion, we obtain,
ΔOAB ≅ ΔODC
⇒∠BOA = ∠COD [Corresponding parts of congruent triangles]
⇒∠BOA = 42°
⇒ x = 42°
Answer⇒ x = 42°
Answer(ii):
x = 8 cm
Step-by-step explanation:
Given:-
- A circle with center O
- ∠POQ = 50°
- ∠ROS = 50°
- RS = 8 cm
Solution:-
In ΔPOQ and ΔSOR, we have
OP = OS, [Both equal to the radius of the circle]
∠POQ = ∠SOR = 50° [Given]
OQ = OR [Both equal to the radius of the circle]
So, by SAS-congruence criterion, we obtain,
ΔPOQ ≅ ΔSOR
⇒PQ = RS [Corresponding parts of congruent triangles]
⇒PQ = 8 cm
⇒ x = 8 cm
Answer⇒ x = 8 cm