Two circles touch each other externally at T .RS is direct common tangent to the two circle touching the circles at Pand Q , ∠TPQ = 42°,∠PQT ( in degrees ) is :
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 48
Concept used :
1. Sum of all the angles of a triangle = 180°
2. Sum of all the angles on a sraight line = 180°
3. Two tangents from same external point are equal.
Solution:
According to the given question,
From the figure,
OP and OT are the two tangents from same external point O
Then OP =OT and ∠OPT = ∠OTP = 42°
In △OPT,
∠OPT + ∠OTP + ∠POT = 180°
42° + 42° + ∠POT = 180°
∠POT = 96°
Now, ∠POT and ∠QOT lies on a sme line, ∠QOT = 180° - 96° = 84°
In △OQT,
∠QOT + ∠QTO + ∠OQT = 180°
2 ∠OQT + 84° = 180°
2 ∠OQT = 96°
∠OQT = 48°
Hence the required angle ∠PQT = ∠OQT = 48°.