Two circles touch each other externally at P AB is a direct common tangent to the two circles A and ...........

Quantitative Aptitude ( CCS) Geometry

Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact and ∠PAB = 35° . Then ∠ABP is is

35°

55°

75°

65°

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Explanation:

Here, ΔAOP,
AO = OP
⇒ ∠PAO = ∠APO = 35°
⇒ ∠AOP = 180° – (2 × 35°) = 110°
⇒ ∠POB = 180° – 110° = 70°
Also, In ΔPOB, BO = OP
⇒ ∠PBO = ∠OPB
= 180° – 70° /2 = 55°
⇒ ∠ABP = 55°