## 8.4.3 Circles III, Paper 1 (Short Questions)

8.4 Circles, SPM Practice (Short Questions) Question 9: In figure above, ABC is a tangent to the circle centre O at B. AED is a straight line. Find the value of y. Solution: ∠ABO = 90o ∠BOE = 2 × 40o = 80o In quadrilateral AEOB, ∠AEO = 360o  – ∠ABO  – ∠BOE – 35o = 360o  – … Read more

## 8.4.2 Circles III, Paper 1 (Short Questions)

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= 180o  – ∠ACB – ∠CBD – ∠ABD y= 180o  – 60o – 25o– 40o = 55o Question 6: In figure above, KPL is … Read more

## 8.4.1 Circles III, Paper 1 (Short Questions)

Question 1: In figure above, FAD is a tangent to the circle with centre O. AEB and OECD are straight lines. The value of y is Solution: ∠OAD = 90o ∠AOD= 180o  – 90o – 34o= 56o y = 56o  ÷ 2 = 28o Question 2: In figure above, PQR is a tangent to the circle QSTU at Q and … Read more

## 8.3.1 Common Tangents (Sample Questions)

Example 1:   In the diagram, ABG and CDG are two common tangents to the circle with centres O and F respectively. Find the values of (a) x,  (b) y,  (c) z.   Solution: (a) In ∆ BFG, angle BFG = ½ × 56o = 28o angle FBG= 90o ← (tangent is 90o to radius) xo+ 28o + 90o = … Read more

## 8.3 Common Tangents

8.3 Common Tangents A common tangent to two circles is a straight line that touches each of the circles at only one point.   1. Intersect at two points (a) Circles of the same size Number of common tangents Properties of common tangents Two common tangents: AB and CD AC = BD AB = CD AB parallel … Read more

## 8.2 Angle between Tangent and Chord

8.2 Angle between Tangent and Chord   1. In the diagram above, ABC is a tangent to the circle at point B.   2. Chord PB divides the circle into two segments, that is, the minor segment PRB and the major segment PQB. 3. With respect to ∠PBA, ∠ PQB is known as the angle subtended by chord … Read more

## 8.1 Tangents to a Circle

8.1 Tangents to a Circle   1. A tangent to a circle is a straight line that touches the circle at only one point and the point is called the point of contact.   2. If a straight line cuts a circle at two distinct points, it is called a secant. The chord is part of … Read more