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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