PA and PB are tangents to the circle with centre O touching it A and B respectively. If angle equals to 25 then angle POB is
Answers
Answer: 65°
Step-by-step explanation:
Given data:
PA and PB are tangents to a circle with centre O touching the circle at A and B.
∠APO = 25°
To find: The value of angle POB
Solution:
Considering the ∆ PAO and ∆PBO, we have
PA = PB …… [∵ the length of the tangents drawn from an external point to a circle are equal ]
OP = OP …… [∵ hypotenuse to both the triangles]
∠ PAO = ∠PBO = 90° …… [∵ A line tangent to a circle is always perpendicular to the radius corresponding to the point of tangency]
∴ By RHS congruency, ∆ PAO ≅ ∆PBO
∴ ∠POB = ∠POA …… (i)
In ∆ PAO, applying angle sum theorem,
∠PAO + ∠APO + ∠POA = 180°
⇒ 90° + 25° + angle POA = 180° …… [∵ given ∠APO = 25°]
⇒ ∠POA = 180° - (90° + 25°)
⇒ ∠POA = 180° - 115° = 65° …… (ii)
From (i) & (ii), we get
∠POB = 65°
Answer:
PA and PB are tangents to the circle with centre O touching it A and B respectively. If angle equals to 25 then angle POB is
Step-by-step explanation:
65