2000 - JAMB Mathematics Past Questions and Answers - page 5

Δ PQR is isosceles

∴∠PRQ = 30^o

Also in Δ PQR
^{^}Q = 180 -(30 + 30)

= 120^o

PQRS is a cyclic quad

∴^{^}S + ^{^}Q = 180(opp ∠s of a cyclic quad)

S + 120 = 180

S = 60^o

In ΔPSR

x + 50 + 60

= 180(sum of ∠s of a Δ)

x + 110 = 180

x = 180 - 110

x = 70^o

The locus of X is the perpendicular bisector of PQ

< QPR = < PRQ = 30^o (PQ = QR)

< SPQ + < QRS = 180^o (supplementary)

80 + < QRS = 180^o = < QRS = 180^o - 80^o = 100^o

< QRP + < PRS = 100^o = 30^o + < PRS = 100^o

= < PRS = 100^o - 30^o = 70^o

(\bigtriangleup)OEN = (\bigtriangleup)OGN

OE = OG = r(radii)

(r - 8)² + 12² = r²

r² - 16r + 64 + 144 = r²

16r = 64 + 144 = r²

16r = 64 + 144 = 208

(\frac{208}{16}) = 13cm

FH = 2FO = 2OH = 2R

= 2 x 13cm

= 26cm

A = (\int^{x = 4}{x = 0}) ydx = (\int^{4}{0}) x²dx = [(\frac{x^3}{3} + c]^{4}_{0})

= (\frac{64}{3}) square units