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In a ∆PQR, S is any point on side QR. Internal bisector of ∠PQS and ∠PSQ meet at I1, Internal bisector of ∠PSR, and ∠PRS meet at I2. If ∠QI1S = 100°, ∠SI2R = 120°, O is orthocentre of ∆PQR, then what is the measure of ∠QOR?
If the ratio of the angles of a triangle is 2 : 4 : 3, then what is the sum of the smallest angle of the triangle and the largest angle of the triangle? A. 120 degrees B. 100 degrees C. 140 degrees D. 110 degrees
In ∆PQR, perpendicular bisectors of each side meet at point C while perpendiculars from each vertex meet at point O. If the sum of ∠QOR and ∠QCR is 230° and ∠PQC is 30°, then what is the measure of ∠R?
In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR =105°, then what is the value of ∠PAR (in degrees)?
In a ∆PQR, C is circum-center and external bisectors of ∠Q and ∠R meet at point X. If I is the incentre of ∆XQR and ∠QIR = 125°, then what is the length of the perimeter of the circum-circle of ∆PQR when the length of arc QR is 36 cm?
In ΔPQR, ∠QPR = 45° and the bisectors of ∠PQR and ∠PRQ meets at O. What is the value (in degrees) of ∠QOR?
In a ΔPQR, ∠PQR is an obtuse angle. The bisectors of the exterior angles at P and Q meet (when RQ and PQ are extended) at U and V respectively. Find the value of ∠PQR, if PU = PT = TV.
In the diagram PQR is a triangle where the bisectors of interior angle ∠PQR and exterior angle ∠PRT intersect at a point S. If ∠QSR = 45°, then what is the value of ∠QPR ?
In ∆PQR, ∠QIR – ∠POQ = 26° where I and O are the incentre and orthocentre of that triangle. If the measure of ∠Q of the triangle is 28° and C is the circle-center of the triangle, then what is the difference between the measure of ∠PIQ and ∠QCR?
Triangle XYZ is similar to triangle RST. Area of triangle XYZ is 2304 cm2 and area of triangle RST is 1296 cm2. If the longest side of the triangle XYZ measures 144 cm, then what will be the measure of the longest side of the triangle RST?