CBSE Class 10 Answered
Tangents PQ and PR are drawn to a circle such that angle RPQ = 30. A chord RS is drawn parallel to the tangent PQ. Find the angle RQS.
Asked by KSHITIJ PAL | 08 Feb, 2014, 07:13: PM
Expert Answer
PQ = PR
Since tangents drawn from an external point to a circle are equal.
And PQR is an isosceles triangle
thus, ∠RQP = ∠QRP
∠RQP + ∠QRP + ∠RPQ = 180° [Angle sum property of a triangle]
2∠RQP + 30° = 180°
2∠RQP = 150°
∠RQP = ∠QRP = 75°
∠RQP = ∠RSQ = 75° [ Angles in alternate Segment Theorem states that angle between chord and tangent is equal to the angle in the alternate segment]
RS is parallel to PQ
Therefore ∠RQP = ∠SRQ = 75° [Alternate angles]
∠RSQ = ∠SRQ = 75°
Therefore QRS is also an isosceles triangle
∠RSQ + ∠SRQ + ∠RQS = 180° [Angle sum property of a triangle]
75° + 75° + ∠RQS = 180°
150° + ∠RQS = 180°
∠RQS = 30°
Answered by | 10 Feb, 2014, 12:27: PM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by yalagondanikhil | 16 Apr, 2024, 12:25: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by jennyy | 26 Mar, 2022, 08:41: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by sowmyashreeiyer | 31 Jan, 2022, 11:40: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by riazu945 | 16 Jan, 2022, 01:00: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by ajabraosable27 | 11 Oct, 2021, 09:28: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by amikasangma080 | 11 Oct, 2021, 06:14: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by muskanmahek2411 | 08 Oct, 2021, 10:48: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by anishasheoran372 | 13 Jul, 2021, 09:33: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by bhilarevishwesh | 21 May, 2021, 08:27: AM
ANSWERED BY EXPERT