What is the length of QC?
Consider the following for the next three (03) items that follow:<br>In the triangle ABC, AB=6 cm, BC=8 cm and AC=10 cm. The perpendicular dropped from B meets the side AC at D. A circle of radius BD (with centre B) cuts AB and BC at P and Q respectively as shown in the figure.
- A. 4.4 cm
- B. 4.2 cm
- C. 3.6 cm
- D. 3.2 cm ✓
Correct Answer: D. 3.2 cm
Explanation
In right \triangle ABC, the altitude BD = \frac{AB \times BC}{AC} = \frac{6 \times 8}{10} = 4.8 cm. Since the circle has radius BD, BQ = 4.8 cm. Thus, QC = BC - BQ = 8 - 4.8 = 3.2 cm.
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