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Two circles touch each other internally at point X. A common chord is drawn to both the circles, which intersects the bigger circle in A and B and the smaller circle in P and Q such that A-P-Q-B. If measure of angle BXQ is 40° what is the measure of angle AXP?
  • a)
    40°
  • b)
    60°
  • c)
    20°
  • d)
    30°
  • e)
    Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two circles touch each other internally at point X. A common chord is ...
As shown in the figure, let us draw a common tangent to both the circles, at the point they touch each other, point X.
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Two circles touch each other internally at point X. A common chord is ...

Solution:

Given:
- Two circles touch each other internally at point X.
- A common chord intersects the bigger circle at A and B, and the smaller circle at P and Q such that A-P-Q-B.
- The measure of angle BXQ is 40 degrees.

To Find:
The measure of angle AXP.

Explanation:
- Since A-P-Q-B is a cyclic quadrilateral, the opposite angles sum up to 180 degrees.
- Therefore, angle AXP = angle AQB (as they are opposite angles in the cyclic quadrilateral).

- In triangle BQX, angle BXQ = 40 degrees (given).
- Angles in a triangle sum up to 180 degrees.
- Therefore, angle BQX = 180 - 40 = 140 degrees.

- In triangle AQB, angle AQB = 180 - angle BQX (angles in a triangle sum up to 180 degrees).
- Therefore, angle AQB = 180 - 140 = 40 degrees.

- Since angle AXP = angle AQB, we have angle AXP = 40 degrees.

Therefore, the measure of angle AXP is 40 degrees.
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Two circles touch each other internally at point X. A common chord is drawn to both the circles, which intersects the bigger circle in A and B and the smaller circle in P and Q such that A-P-Q-B. If measure of angle BXQ is 40° what is the measure of angle AXP?a)40°b)60°c)20°d)30°e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
Question Description
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