# Circles Short Questions (Question 5 - 8)

Question 5:
In figure above, PAQ is a tangent to the circle at point A. AEC and BED are straight lines. The value of y is

Solution:
ABD ACD = 40o
ACB PAB = 60o
y = 180– ACB – CBD – ABD
y = 180– 60o – 25o – 40o = 55o

Question 6:
In figure above, KPL is a tangent to the circle PQRS at point P. The value of x is

Solution:
PQS = SPL = 55o
SPQ = 180– 30o – 55o = 95o
SPQ + SRQ = 180o
95o + xo = 180o
x = 85o

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 = 45o
QPR = (180– 45o) ÷ 2 = 67.5o
PQR + BPQ + xo = 180o
45o + (67.5o + 45o) + xo = 180o
x = 22.5o

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: