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Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. The value of ∠ L APB is - Mathematics

Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. The value of ∠ L APB is

(A) 30°

(B) 45°

(C) 60°

(D) 90°

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Solution

Correct answer: D

TA = TP ⇒ ∠TAP = ∠TPA
TB = TP ⇒∠TBP = ´TPB
∠TAP + ∠TBP

Correct answer: D

TA = TP ⇒ ∠TAP = ∠TPA
TB = TP ⇒∠TBP = ´TPB
∠TAP + ∠TBP= ∠TPA + ∠TPB= ∠APB

` ∠TAP + ∠TBP+ ∠APB=180^@[because "sum of" ......180^@]`

`/_APB+/_APB=180^@`

`2/_APB=180^@`

`/_APB=90^@`

 

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