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RV-23-001 · Circle chord: reverse radius and exact area

AB is a chord of a circle with centre O. M is the midpoint of AB. AB = 16 cm and OM = 7 cm.
ABMO7 cmr cm
Diagram not accurately drawn

(a) Find the radius of the circle. Give an exact answer.

(b) Find the area of the circle and the area of triangle OAB. Give exact answers.

Part (a) Circle Chord Perpendicular Bisector, Pythagoras & Exact Area Booklet p. 34, p. 37 & p. 85
Method
1) Line from centre O to midpoint M of chord is perpendicular (90°)
2) Use Pythagoras r² = AM² + OM²
3) Circle area = πr², Triangle area = ½ × AB × OM
Worked Example (RV-23-001 · Part (a))
Find the radius of the circle. Give an exact answer.
1)
OM is perpendicular to AB, because the line from the centre to the midpoint of a chord is perpendicular to it.
2)
AM = 8; r² = 8² + 7².
3)
113\sqrt{113} cm
Ans = 113\sqrt{113} cm
Part (b) Circle Chord Perpendicular Bisector, Pythagoras & Exact Area Booklet p. 34, p. 37 & p. 85
Method
1) Line from centre O to midpoint M of chord is perpendicular (90°)
2) Use Pythagoras r² = AM² + OM²
3) Circle area = πr², Triangle area = ½ × AB × OM
Worked Example (RV-23-001 · Part (b))
Find the area of the circle and the area of triangle OAB. Give exact answers.
1)
Circle area = πr².
2)
113π113\pi cm²
3)
Triangle area = ½ × 16 × 7 = 56 cm².
Ans = 113π113\pi cm²; 56 cm².