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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)`∠`Qpr . - 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)`∠`QPR .

Solution

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

i) Now arc RQ subtends`∠`QOR at the centre and `∠`QPR at the remaining part of the circle. 

∴ `∠`QPR = `1/2` `∠` QOR

⇒ `∠`QPR = `1/2 xx120°`

⇒ `∠` QPR = 60°

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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)`∠`Qpr . 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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