11. In a right-angled triangle, the length 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)?
12. Three sides of a triangle measure 6 cm, 10 cm and x cm. The minimum integral value of x is:
13. In the given triangle, D and E are the mid-points of AF and AG, F and G are the mid-points of AB and AC. If DE = 2.4 cm, then value of BC is:-
14. In the given figure, a circle touches the sides of the quadrilateral PQRS. The radius of the circle is 9 cm. ∠RSP = ∠SRQ = 60° and ∠PQR = ∠QPS = 120°. What is the perimeter (in cm) of the quadrilateral?
15. ln ΔABC, M is midpoint of the side AB. N is a point in the interior of ΔABC such that CN is the bisector of ∠C and CN ⊥ NB. What is the length (in cm) of MN, if BC = 10 cm and AC = 15 cm?
16. ABC is an isosceles right angle triangles having ∠C = 90°. If D is mid point on AB, then AD2 + BD2 is equal to
17. What is the distance between two parallel tangents of a circle of radius 8 cm?
18. In the given figure, in triangle STU, ST = 8 cm, TU = 9 cm and SU = 12 cm. QU = 24 cm, SR = 32 cm and PT = 27 cm. What is the ratio of the area of triangle PQU and area of triangle PTR?
19. In a triangle PQR, PX, QY and RZ be altitudes intersecting at O. If PO = 6 cm, PX = 8 cm and QO = 4 cm, then what is the value (in cm) of QY?
20. Three circle C1, C2 and C3 with radii r1, r2 and r3 (where r1 < r2 < r3) are placed as shown in the given figure. What is the value of r2?
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