Multiple choice

If PQ and PR are the two tangents to a circle with centre O, which of the following relationships is true?

  1. PO = OQ

  2. OQ = RP

  3. OQ2 = OR2 + RP2

  4. PQ2 + OR2 = OP2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For tangents PQ and PR from point P to a circle with center O, the radius OQ is perpendicular to tangent PQ. Thus, triangle OQP is a right-angled triangle with hypotenuse OP. By Pythagorean theorem, OQ^2 + PQ^2 = OP^2.

AI explanation

The radius is perpendicular to the tangent at the point of contact, making triangle OQP a right angled triangle with the right angle at Q. By the Pythagorean theorem, the square of the hypotenuse OP equals the square of side PQ plus the square of side OQ. Since OQ and OR are both radii of the circle, OQ squared equals OR squared, making PQ squared plus OR squared equal to OP squared. This confirms the correct relationship is PQ squared plus OR squared equals OP squared.

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