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In a Triangle Abc, the Incircle (Centre O) Touches Bc, Ca and Ab at Points P, Q and R Respectively. Calculate : (I) `∠`Qor - ICSE Class 10 - Mathematics

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ConceptTangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments

Question

In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate : (i) `∠`QOR

Solution

The incircle touches the sides of the triangle ABC and
OP ⊥  BC,OQ ⊥ AC,OR ⊥ AB

 i) In quadrilateral AROQ,
`∠`ORA = 90°  ,`∠`OQA = 90°  ,`∠`A = 60°
`∠`QOR = 360°  - (90°  + 90° + 60° )

`∠`QOR = 360° -  240°
`∠`QOR = 120° 

  Is there an error in this question or solution?

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Solution In a Triangle Abc, the Incircle (Centre O) Touches Bc, Ca and Ab at Points P, Q and R Respectively. Calculate : (I) `∠`Qor Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.
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