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