SPM Practice (Short Questions)

Posted on April 23, 2020 by user

Question 7:

In figure above, APB is a tangent to the circle PQR at point P. QRB is a straight line. The value of x is

Solution:

∠PQR = ∠RPB = 45^o

∠QPR = (180^o– 45^o) ÷ 2 = 67.5^o

∠PQR + ∠BPQ + x^o = 180^o

45^o+ (67.5^o + 45^o) + x^o = 180^o

x = 22.5^o

Question 8:

The figure above shows two circles with respective centres O and V. AB is a common tangent to the circles. OPRV is a straight line. The length, in cm, of PR is

Solution:

$\begin{array}{l} \cos 86^{o} = \frac{O M}{O V} \\ 0.070 = \frac{1}{O V} \\ O V = \frac{1}{0.070} \\ O V = 14.29 c m \\ ∴ P R = 14.29 - 5 - 4 \\ = 5.29 c m \end{array}$