Circle Theorems (Copy)
Q1 (Non-Calculator)
In a circle, a triangle is drawn where one side is the diameter.
One of the angles at the circumference is x°.
Find the value of x.
Solution:
Angle in a semicircle = 90°
x = 90°
Answer:
90°
Q2 (Non-Calculator)
In a circle, AB is the diameter and C is a point on the circle.
Find the measure of angle ACB.
Solution:
Angle in a semicircle = 90°
Angle ACB = 90°
Answer:
90°
Q3 (Non-Calculator)
A line is tangent to a circle at point P.
The radius to point P is drawn.
Find the angle between the radius and the tangent.
Solution:
Angle between tangent and radius = 90°
Answer:
90°
Q4 (Non-Calculator)
In a circle, O is the centre, and PT is a tangent at point P.
Find the angle OPT, where O is the centre and T is a point on the tangent.
Solution:
Radius is perpendicular to tangent.
Angle OPT = 90°
Answer:
90°
Q5 (Non-Calculator)
A triangle is drawn inside a circle such that one side is a diameter.
The other two sides meet at a point on the circumference.
If one of the other angles is 35°, find the third angle.
Solution:
- Angle at circumference opposite diameter = 90°
- Sum of angles in triangle = 180°
- Third angle = 180 – 90 – 35
- Third angle = 55°
Answer:
55°
Q6 (Calculator)
In a circle, AB is the diameter, and D lies on the circle.
If angle ADB = x°, find x.
Solution:
Angle in a semicircle = 90°
x = 90°
Answer:
90°
Q7 (Calculator)
In a circle, a radius OP meets a tangent at P.
If angle between OP and the tangent is x°, find x.
Solution:
Angle between radius and tangent = 90°
x = 90°
Answer:
90°
Q8 (Calculator)
A triangle is drawn inside a circle with one side as diameter PQ.
The third point R lies on the circumference.
If angle PQR = 90°, what is the name of triangle PQR?
Solution:
Triangle PQR is a right-angled triangle.
Answer:
Right-angled triangle
Q9 (Calculator)
In a circle, a chord AB is drawn.
Is the angle at the centre O between radius OA and a tangent at A equal to 90°?
Solution:
Yes, because the tangent at any point is perpendicular to the radius at that point.
Answer:
Yes, 90°
Q10 (Calculator)
A circle has a tangent at point A and a radius OA.
If the radius OA is 5 cm long, what is the length from O to the tangent line at A?
Solution:
The radius itself is the shortest distance and meets the tangent at 90°.
Distance = radius = 5 cm
Answer:
5 cm