1.

In the figure above, PQ=QR and ∠Q = ∠SRP = 36°. If ∠TPR = 54°, find ∠STP.
a) 24°               b)27°              c)18°               d)36°

2.If s is the semiperimeter of a triangle with sides as a, b and c. Then which of the following is true?

a) (s-a)(s-b)(s-c)>abc/8

b) (s-a)(s-b)(s-c)<abc/8

c) (s-a)(s-b)(s-c)≤ abc/8

d) (s-a)(s-b)(s-c)≥ abc/8

3.Two sides of a right triangle are 6 and 8 and the in-radius is 2, What is the circum-radius?

a) 10             b) 4              c)5                d)6

4.

The   ΔPQR is formed by extending the lines AB, BC and CA of the ΔABC. If AC is 10 cm and CP is 30cm, AB is 14cm and AR is 35 cm also, BC is 12 cm while QB is 48 cm.

What is the ratio of area of ΔABC to area of ΔPQR?

a)2:31             b)2:29                 c)1:20               d) 1:37

5. In an equilateral triangle ΔPQR has the area of 120 sq units. Medians RS and QT are drawn intersecting at O. What is the area of triangle ΔSTO in sq units?

a)12                   b)10                  c)30                    d)None of these

6. PQR is a right triangle, right angled at Q. The circle inscribed in the triangle, with radius of 6 units, touches the side PQ at S. If PS=14 units, find the length of PR.

a)27 units           b)29 units          c)35 units                 d)23 units

7.In ΔPQR, S is the midpoint of  QR. Point T is on PQ such that PT:TQ is 3:2 and point U is on PR such that PU:UR = 3:7. It TU and PS intersect at V, what is the ratio of area of ΔVTS to area of ΔUVS?

a)2:1                     b)3:5                   c)2:1                       d)5:3

8.

In the figure, PSTU is a cyclic quadrilateral and QS=SP, TU=TR ,  SV=PV=QV. How many of the statements would always be true?

i) PS is the median of ΔPQR

ii) ΔSQV and ΔSPV are congruent

iii)The orthocenter of ΔPQR lies at point P.

a) 1                b)2                    c)3                  d) Cannot be determined

9.In a ΔABC, M is the midpoint of AB and N is the midpoint of AC. CM and BN are perpendicular to each other  and meet at point O. If AB 14 and AC is √54 , find BC.

a) 5√7          b) 4√2          c) 2√7           d) 5√2

10.

Find the sum of all angles shown. P + Q + R+S+T +U+V +W

a)360°               b) 1080°               c) 1000°                 d) 720°