Angles and Tangents of Circles

Question 9:   In figure above, ABC is a tangent to the circle centre O, at point B. The value of x is Solution: ∠OBC = 90o  ∠BOD = 2 × 50o = 100o In quadrilateral BODC, xo = 360o  – ∠BOD – ∠OBC – 120o = 360o  – 100o – 90o – 120o = 50 Question 10: … Read more

Question 7: In figure above, ABCD is a tangent to the circle CEF at point C. EGC is a straight line. The value of y is   Solution: ∠ C E F = ∠ D C F = 70 ∘ ∠ A E G + 70 ∘ + 210 ∘ = 360 ∘ ∠ A E … Read more

Question 4: 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 5: In figure above, KPL is … Read more

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

Question 7: Diagram below shows a circle with centre O. Find the value of x. Solution: ∠ Q R O = 38 o , ∠ O R S = 44 o ∠ Q R S = 38 o + 44 o = 82 o x o = 82 o × 2 x o = 164 … Read more

6.6.2 Angles and Tangents of Circles, PT3 Practice Question 4: Diagram below shows a circle with centre O. POR is a straight line. Find the value of x and of y. Solution: x = 40 × 2 = 80 y = 180 − 80 2 = 50 Question 5: Diagram below shows a semicircle ABCD with … Read more

6.6.1 Angles and Tangents of Circles, PT3 Practice Question 1: (a) In Diagram below, KLM, LPN and MPO are straight lines.   Find the value of x and of y. (b) In the diagram below, O is the centre of the circle. Find the value of (i) x   (ii) y   Solution: (a) ∠ L O M = ∠ … Read more

6.5.1 Common Tangents (II) 3. Do not intersect (a) Circles of the same size Number of common tangents Properties of common tangents Four common tangents: AB, CD, PS and RQ AB = CD = OV PS = RQ AB // OV // CD (b) Circles of different sizes   Number of common tangents Properties of … Read more

6.5.1 Common Tangents (I) 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 … Read more

Example 1: In the diagram, PQR is a tangent to the circle QSTU at Q. Find the value of y.   Solution: Angle QUT  = 180o– 98o ← (opposite angle in cyclic quadrilateral QSTU ) = 82o Angle QTU = 75o  ← (angle in alternate segment) Therefore y= 180o – (82o + 75o)  ← (Sum of … Read more