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Two circles touch externally at P. QR is a common tangent of the circles touching the circles at Q and R. Then measure of ∠QPR is
Answer & Solution
Correct Answer:
Option
C
According to question
QR is the common tangent and NO is also the common tangent.
∴ QN = NP = NR
In ΔQPN
∠NQP = ∠NPQ
∠NRP = ∠NPR
In ΔPQR
∠P + ∠Q + ∠R = 180°
x + y + x + y = 180°
2x + 2y = 180°
x + y = 90°
As shown in the figure x + y = ∠P = 90°
QR is the common tangent and NO is also the common tangent.
∴ QN = NP = NR
In ΔQPN
∠NQP = ∠NPQ
∠NRP = ∠NPR
In ΔPQR
∠P + ∠Q + ∠R = 180°
x + y + x + y = 180°
2x + 2y = 180°
x + y = 90°
As shown in the figure x + y = ∠P = 90°
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