For the following questions answer them individually
I and 0 are respectively the in-centre and circumcentre of a triangle ABC. The line AI produced intersects the circumcircle of ΔABC at the point D. If ∠ABC = x°, ∠BID = y° and ∠BOD = z°, then $$\frac{z+x}{y}=$$
Rana drove 8 miles due west, then 6 miles due north, then 3 miles due east and then 6 more miles due north. The distance between his initial and final position is
In ΔABC and Δ DEF. AB = DE and BC = EF. Then one can infer that Δ ABC ≅ Δ DEF, when
The length of the common chord of two circles of radii 30 cm and 40 cm whose centres are 50 cm apart, is (in cm)
Two chords AB, CD of a circle with centre 0 intersect each other at P. ∠ADP = 23° and ∠APC = 70°, then the ∠BCD is
If the interior angles of a five-sided polygon are in the ratio of 2 : 3 : 3 : 5 : 5, then the measure of the smallest angle is
If sin (60° - θ) = cos (Ψ - 30°), then the value of tan (Ψ - θ) is (assume that θ and Ψ are both positive acute angles with θ < 60° and Ψ > 30°).
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