Chord BC is drawn in a circle with a radius of 3cm. Chord BS is 4cm long. Find the perpendicular distance from A to chord BC
make a sketch and you should see a nice right-angled triangle with base of 3, hypotenuse of 3
Use Pythagoras to find the height.
To find the perpendicular distance from point A to chord BC, we can use a property of chords in a circle.
Step 1: Draw the radius from the center (O) of the circle to the midpoint (M) of chord BC. Let's label the point where the radius intersects chord BC as point D.
Step 2: Since BD is the perpendicular bisector of chord BC, we know that triangle BDM is a right triangle.
Step 3: We can use the Pythagorean theorem to find the length of DM. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length of the hypotenuse BD is 3 cm (the radius of the circle), and we know that BS (the other side of the right triangle) is 4 cm. So we have:
BD² = DM² + BS²
(3 cm)² = DM² + (4 cm)²
9 cm² = DM² + 16 cm²
25 cm² = DM²
Step 4: Take the square root of both sides to find the length of DM:
DM = √25 cm²
DM = 5 cm
Step 5: Now, we know that the distance from A to chord BC is equal to half the length of DM. So the perpendicular distance from A to chord BC is:
Perpendicular distance = DM / 2
Perpendicular distance = 5 cm / 2
Perpendicular distance = 2.5 cm
Therefore, the perpendicular distance from point A to chord BC is 2.5 cm.