Atempt any two of the following :
In `DeltaPQR` ray MX and ray MY bisect `anglePMQ and anglePMR` respectively . P- X - Q , P - Y - R . Seg PM is a median , prove that seg XY || seg QR

Solve the any one of following sub questions: In Delta PQR, "seg" PM "is a median" PM = 10 and PQ^(2) + PR^(2) = 328 "then find" QR

In DeltaXYZ, XY=YZ. "Ray YM bisects" angleXYZ. X-M-Z prove that M is midpoints of seg XZ.

Atempt any two of the following : In the adjoining figure , in the adjoining figure , in Delta ABC, A-P-Band A-Q-C "Prove that " (A(DeltaAPQ))/(A(DeltaABC))=(APxxAQ)/(ABxxAC)

Perform any one the following activities: In the adjoining figure , seg PM is a median . Prove that A(DeltaPQM)=A(DeltaPRM)

In the adjoining figure the circles with centers P and Q touch each other at R . A line passing through R meets the circles at A and B respectively then Prove that : (i) seg AP|| seg BQ. (ii) DeltaAPR~DeltaRQB . (iii) Find angleRQB if anglePAR = 35^(@)

Let C_1 and C_2 be parabolas x^2 = y - 1 and y^2 = x-1 respectively. Let P be any point on C_1 and Q be any point C_2 . Let P_1 and Q_1 be the reflection of P and Q, respectively w.r.t the line y = x then prove that P_1 lies on C_2 and Q_1 lies on C_1 and PQ >= [P P_1, Q Q_1] . Hence or otherwise , determine points P_0 and Q_0 on the parabolas C_1 and C_2 respectively such that P_0 Q_0 <= PQ for all pairs of points (P,Q) with P on C_1 and Q on C_2

Let E1 and E2, be two ellipses whose centers are at the origin.The major axes of E1 and E2, lie along the x-axis and the y-axis, respectively. Let S be the circle x^2 + (y-1)^2= 2 . The straight line x+ y =3 touches the curves S, E1 and E2 at P,Q and R, respectively. Suppose that PQ=PR=[2sqrt2]/3 .If e1 and e2 are the eccentricities of E1 and E2, respectively, then the correct expression(s) is(are):

Attempt any Two of the following: In squareABCD ,seg AB ||seg CD . Diagonal AC and BD intersect each other at point P . Prove : (A(DeltaABP))/(A(DeltaCPD))=(AB^(2))/(CD^(2))

In DeltaPQR , ray QS bisects of anglePQR.P-S-R . Show that (A(DeltaPQS))/(A(DeltaQRS))=(PQ)/(QR)

Let ABC be an equilateral triangle inscribed in the circle x^2+y^2=a^2 . Suppose pendiculars from A, B, C to the ellipse x^2/a^2+y^2/b^2=1,(a > b) meets the ellipse respectivelily at P, Q, R so that P, Q , R lies on same side of major axis as A, B, C respectively. Prove that the normals to the ellipse drawn at the points P Q nad R are concurrent.