Geometry Practice Test 2

Question : 33 of 40

Marks: +1, -0

O and C are respectively the orthocenter and circumcentre of an acute angled triangle PQR. The points P and O are joined and produced to meet the side QR at S. If ∠PQS = 60° and ∠QCR = 130°, then ∠RPS = ?

30°
35°
100°
60°

Validate

Solution:

2∠QCR = ∠QPR
∠QCD =

{130}/2

= 65°

In ΔPQR,
∠P +∠Q+∠R = 180°
65° + 60° +∠R = 180°
∠R = 55°
In ΔPSR,
∠SPR +∠PSR +∠SRP = 180°
∠SPR = 180° −190° + 55°)
∠SPR = 35°

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