1. In \(\triangle\)ABC, if AB = \((2a-1)\) cm, AC = \(2\sqrt{2}a\) cm, and BC = \((2a+1)\) cm, then write the value of \(\angle\)BAC.

2. In \(\triangle\)ABC, if AB \(= (2p-1)\) cm, AC \(= 2\sqrt2p\) cm, and BC \(= (2p+1)\) cm, then the value of \(\angle\)BAC is...? Let me know if you need further assistance!

3. In triangle ABC, AB = (2a − 1) cm, AC = 2√2a cm, and BC = (2a + 1) cm. Find the measure of ∠BAC.

4. In triangle ABC, a straight line parallel to side BC intersects AB at point P and AC at point Q. If AP = 4 cm, QC = 9 cm, and PB = AQ, then find the length of PB.

5. In \(\triangle\)ABC, \(\angle\)ABC = 90° and BD \(\perp\) AC. If BD = 6 cm and AD = 4 cm, then find the length of CD.

6. In triangle ABC, DE || BC, where D and E lie on sides AB and AC respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, then find the length of AC.

7. In triangle ABC, if AB = (2a−1) cm, AC = \(2\sqrt{2}a\) cm, and BC = (2a+1) cm, then write the value of ∠BAC.

8. From point A of triangle ABC, a perpendicular AD is drawn to side BC, meeting at point D. If BD = 8 cm, DC = 2 cm, and AD = 4 cm, then write the measure of ∠BAC.

9. In the adjacent figure, triangle ABC is inscribed in a circle and touches the circle at points P, Q, and R. If AP = 4 cm, BP = 6 cm, AC = 12 cm, and BC = x cm, then find the value of x.

10. Triangle ABC is inscribed in a circle, and the circle touches the sides at points P, Q, and R respectively. If AP = 4 cm, BP = 6 cm, and AC = 12 cm, then find the length of BC.

11. In triangle ABC, ∠ABC = 90° and BD ⊥ AC; If BD = 16 cm and AD = 10 cm, then find the length of CD.