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In the Given Figure, Two Circles Touch Each Other Externally at Point P. Ab is the Direct Common Tangent of These Circles. Prove That: (Ii) Angles Apb = 90° - ICSE Class 10 - Mathematics

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ConceptTangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers

Question

In the given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Prove that: 

(ii) angles APB = 90°

 

Solution

ii) Now in Δ ATP ,
∴ `∠`TAP = `∠`TPA
Similarly in Δ BTP,`∠`TBP = `∠`TPB
Adding,
`∠`TAP +`∠`TBP =`∠`APB
But
∴ TAP + `∠`TBP  + `∠`APB =180°
⇒ `∠`APB =  `∠`TAP  + `∠`TBP =90°

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Solution In the Given Figure, Two Circles Touch Each Other Externally at Point P. Ab is the Direct Common Tangent of These Circles. Prove That: (Ii) Angles Apb = 90° Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers.
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