Question:
In the above figure, ACB is a right-angled triangle. CD is the altitude. Circles are inscribed within the triangles \( \triangle ACD \) and \( \triangle ABC \). P and Q are the centres of the circles. The distance PQ is
In the above figure, ACB is a right-angled triangle. CD is the altitude. Circles are inscribed within the triangles \( \triangle ACD \) and \( \triangle ABC \). P and Q are the centres of the circles. The distance PQ is
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In right-angled triangles with inscribed circles, use the geometric properties and the distances between the circle centers to find the required distances.
Updated On: Aug 4, 2025
- 5
- \( \sqrt{50} \)
- 3.7
- 4.8
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The Correct Option is B
Solution and Explanation
Given that \( \triangle ACB \) is a right triangle and \( CD \) is the altitude, we can use the geometric properties of the incircles in the two smaller triangles formed by the altitude. The distance \( PQ \) between the centres of the circles is equal to \( \sqrt{50} \). Thus, the Correct Answer is \( \sqrt{50} \).
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