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Tangents, Chords & Secant Segments — Easy Worksheet 2
Grade 10 · Whoobee Name: ____________________ Date: __________
O is the center of each circle. Lines that look tangent are tangent. Find x.
How to solve
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Example
PA is tangent to circle O at A. Find x.
Answer: 3
Not quite. The answer is
💡 A tangent is perpendicular to the radius at the point of tangency, so ∠OAP = 90° and OP is the hypotenuse. By the Pythagorean Theorem, OA2 + PA2 = OP2. x2 = 52 + 122 = 25 + 144 = 169, so x = √169 = 13.
✓ Correct!
Not quite. The answer is
💡 A tangent is perpendicular to the radius at the point of tangency, so ∠OAP = 90° and OP is the hypotenuse. By the Pythagorean Theorem, OA2 + PA2 = OP2. x2 = 52 + 122 = 25 + 144 = 169, so x = √169 = 13.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Two tangent segments drawn to a circle from the same outside point are congruent, so PA = PB. PA = 23, so x = 23.
✓ Correct!
Not quite. The answer is
💡 Two tangent segments drawn to a circle from the same outside point are congruent, so PA = PB. PA = 23, so x = 23.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Intersecting Chords Theorem, the products of the chord pieces are equal: AE × EB = CE × ED. 12 × x = 8 × 6, so 12x = 48. Divide both sides by 12: x = 48 ÷ 12 = 4.
✓ Correct!
Not quite. The answer is
💡 By the Intersecting Chords Theorem, the products of the chord pieces are equal: AE × EB = CE × ED. 12 × x = 8 × 6, so 12x = 48. Divide both sides by 12: x = 48 ÷ 12 = 4.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A tangent is perpendicular to the radius at the point of tangency, so ∠OAP = 90° and OP is the hypotenuse. By the Pythagorean Theorem, OA2 + PA2 = OP2. x2 = 152 − 92 = 225 − 81 = 144, so x = √144 = 12.
✓ Correct!
Not quite. The answer is
💡 A tangent is perpendicular to the radius at the point of tangency, so ∠OAP = 90° and OP is the hypotenuse. By the Pythagorean Theorem, OA2 + PA2 = OP2. x2 = 152 − 92 = 225 − 81 = 144, so x = √144 = 12.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Two tangent segments drawn to a circle from the same outside point are congruent, so PA = PB. PA = 22, so x = 22.
✓ Correct!
Not quite. The answer is
💡 Two tangent segments drawn to a circle from the same outside point are congruent, so PA = PB. PA = 22, so x = 22.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Intersecting Chords Theorem, the products of the chord pieces are equal: AE × EB = CE × ED. 8 × 5 = 10 × x, so 10x = 40. Divide both sides by 10: x = 40 ÷ 10 = 4.
✓ Correct!
Not quite. The answer is
💡 By the Intersecting Chords Theorem, the products of the chord pieces are equal: AE × EB = CE × ED. 8 × 5 = 10 × x, so 10x = 40. Divide both sides by 10: x = 40 ÷ 10 = 4.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A tangent is perpendicular to the radius at the point of tangency, so ∠OAP = 90° and OP is the hypotenuse. By the Pythagorean Theorem, OA2 + PA2 = OP2. x2 = 52 − 32 = 25 − 9 = 16, so x = √16 = 4.
✓ Correct!
Not quite. The answer is
💡 A tangent is perpendicular to the radius at the point of tangency, so ∠OAP = 90° and OP is the hypotenuse. By the Pythagorean Theorem, OA2 + PA2 = OP2. x2 = 52 − 32 = 25 − 9 = 16, so x = √16 = 4.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Intersecting Chords Theorem, the products of the chord pieces are equal: AE × EB = CE × ED. 15 × 6 = x × 10, so 10x = 90. Divide both sides by 10: x = 90 ÷ 10 = 9.
✓ Correct!
Not quite. The answer is
💡 By the Intersecting Chords Theorem, the products of the chord pieces are equal: AE × EB = CE × ED. 15 × 6 = x × 10, so 10x = 90. Divide both sides by 10: x = 90 ÷ 10 = 9.
💡 How to solve: Tangents, Chords & Secant Segments
A tangent is perpendicular to the radius at the point of tangency, so use the Pythagorean Theorem. Two tangent segments from the same point are equal. For two chords that cross: part × part = part × part. For two secants from an outside point: outside × whole = outside × whole. For a tangent and a secant: tangent2 = outside × whole.
Try a similar one
PA is tangent to circle O at A. Find x.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Tangents, Chords & Secant Segments — Easy Worksheet 2
O is the center of each circle. Lines that look tangent are tangent. Find x.