SSC CGL 2022111)A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R, respectively: If AB - BC = 4 cm, AB - AC = 2 cm and the perimeter of ΔABC = 32 cm, then \(BC \over 2\) (in cm) = ?
\(13 \over 3\)
SSC CGL 2022112)In a triangle ABC, the bisector of angle BAC meets BC at point D such that DC = 2BD. If AC - AB = 5 cm, then find the length of AB (in cm).
5
SSC CGL 2022113)In a right-angled triangle, the lengths of the medians from the vertices of acute angles are 7 cm and \( 4\sqrt 6\) cm. What is the length of the hypotenuse of the triangle (in cm)?
\(2\sqrt{29}\)
SSC CGL 2022114)In a right triangle ABC, right angled at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5 cm, then find the value of AB2 + BD2 (in cm).
96
SSC CGL 2022115)A triangle with the lengths of its sides proportional to the numbers 7, 24 and 30 is:
obtuse angled
SSC CGL 2022116)In ΔPQR, ∠Q = 66° and ∠R = 34. T is a point on QR , and S is a point between Q and T such that PS ⊥ QR and PT is the bisector of ∠QPR. What is the measure of ∠SPT?
16
SSC CGL 2022117)In triangle ABC, X and Y are the points on sides AB and AC, respectively, such that XY is parallel to BC. If XY : BC = 2.5 : 7, what is the ratio of the area of the trapezium BCYX to that of the ΔAXY?
\(171\over25\)
SSC CGL 2022118)In △ABC, ∠A = 68°. If I is the incentre of the triangle, then the measure of ∠BIC is:
124°
SSC CGL 2022119)In a right-angled triangle PQR, ∠Q = 90°. A and B are the mid-points of PQ and PR, respectively. If PQ = 16 cm, QR = 30 cm and PR = 34 cm, what is perimeter (in cm) of the trapezium ABRQ?
70
SSC CGL 2022120)In a ΔABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 25.6 cm, CA = 18.8 cm and AB = 20.4 cm, what is the perimeter (in cm) of the ΔDEF?
32.4