**Q) In the given figure, AB and CD are tangents to a circle centred at O. Is angle BAC = angle DCA ? Justify your answer.**

**Ans: **

**Step 1:** Let’s connect center O with points A and C

**Step 2:** Since BA is the tangent to the circle and OA is the radius of the circle,

∴ ∠ OAB = 90

Similarly, DC is the tangent to the circle and OC is the radius of the circle,

∴ ∠ OCD = 90

**Step 3: ** Next, we look at Δ OAC:

Since OA and OC are radii of the circle

∴ the angles opposite to the equal sides are always equal

∴ ∠ OAC = ∠ OCA

**Step 4:** Next, we look in Δ OAC

∠ BAC = ∠ OAB + ∠ OAC

= ∠ OCD + ∠ OCA

= ∠ DCA

**∴ ∠ BAC = ∠ DCA**

**Hence Proved !**

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