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The Given Figure Shows a Circle with Centre O Such that Chord Rs is Parallel to Chord Qt, Angle Prt = 20° and Angle Poq = 100°. Calculate: (I) Angle Qtr - ICSE Class 10 - Mathematics

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ConceptArc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse

Question

The given figure shows a circle with centre O such that chord RS is parallel to chord QT, angle PRT = 20° and angle POQ = 100°. Calculate:

(i) angle QTR

Solution

Join PQ, RQ and ST.

i)
`∠`POQ  + `∠`QOR =  180°
⇒ 100° +  `∠`QOR  = 180°
⇒ `∠`QOR =  80°
Arc RQ subtends `∠`QOR at the centre and `∠`QTR at the remaining part of the circle.

∴ `∠QTR =1/2  ∠QOR`

⇒ `∠QTR =  1/2 xx 80° = 40°`

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Solution The Given Figure Shows a Circle with Centre O Such that Chord Rs is Parallel to Chord Qt, Angle Prt = 20° and Angle Poq = 100°. Calculate: (I) Angle Qtr Concept: Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse.
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