Question 1. In the figure, if ∠ ACB = 35°, then find the measure of ∠ OAB.
Solution: ∠AOB = 180° - (∠1 + ∠2)
= 180° - (35° + 35°) [∵ AO = OB ∴ ∠1 = ∠2]
∠ACB = (1/2)(∠AOB) = (1/2) (110°) = 55°
Question 2. If points A, B and C are such that AB ⊥ BC and AB = 12 cm, BC = 16 cm. Find the radius of the circle passing through the points A, B and C.
Solution: ∵ AB ⊥ BC
∴ ∠B = 90° [Angle in a semicircle]
⇒ AC is a diameter
AC = 20
Radius = 10cm
Question 3. The angles subtended by a chord at any two points of a circle are equal. Write true or false for the above statement and justify your answer.
Solution: False. If two points lie in the same segment only, then the angles will be equal otherwise they are not equal.
Question 4. Two chords of a circle of length 10 cm and 8 cm are at the distance 8.0 cm and 3.5 cm, respectively from the centre, state true and false for the above statement.
Solution: False. As the larger chord is at smaller distance from the centre.