10. In Fig. 10.17, XY and X'Y' are two parallel tangents to a circle w

1.	10. In Fig. 10.17, XY and X'Y' are two parallel tangents to a circle with centre O and another tangenAB with point of contact C intersecting XY at A and X' Y' at B. Prove that < AOB = 90°0x'
Answer» Join OC In Δ OPA and Δ OCA OP = OC (radii of same circle) PA = CA (length of two tangents) AO = AO (Common) Therefore, Δ OPA ≅ Δ OCA (By SSS congruency criterion) Hence, ∠ 1 = ∠ 2 (CPCT) Similarly ∠ 3 = ∠ 4 Now, ∠ PAB + ∠ QBA = 180° 2∠2 + 2∠4 = 180° ∠2 + ∠4 = 90° ∠AOB = 90° (Angle sum property)

10. In Fig. 10.17, XY and X'Y' are two parallel tangents to a circle with centre O and another tangenAB with point of contact C intersecting XY at A and X' Y' at B. Prove that < AOB = 90°0x'

Answer»

Join OC

In Δ OPA and Δ OCA

OP = OC (radii of same circle)

PA = CA (length of two tangents)

AO = AO (Common)

Therefore, Δ OPA ≅ Δ OCA (By SSS congruency criterion)

Hence, ∠ 1 = ∠ 2 (CPCT)

Similarly ∠ 3 = ∠ 4

Now, ∠ PAB + ∠ QBA = 180°

2∠2 + 2∠4 = 180°

∠2 + ∠4 = 90°

∠AOB = 90° (Angle sum property)