Q) In the given figure, Δ ABC is circumscribing a circle. Find the length of BC, if AR = 4 cm, BR = 3 cm and AC = 11 cm.
Ans:
Step 1: We know that, the tangents on a circle from a point are equal
Therefore, the tangents BP and BR, tangents to circle drawn from point B will be equal
∴ BP = BR
∴ BP = 3 cm (given BR = 3 cm)
Step 2: Similarly, AR & AQ are the tangents to circle drawn from point A
∴ AQ = AR
∴ AQ = 4 cm (given AR = 4 cm)
Step 3: From the diagram, we can see that AC = AQ + QC
∴ QC = AC – AQ
∴ QC = 11 – 4 (given AC = 11 cm; AQ = 4 cm – calculated above in step 2)
∴ QC = 7 cm
Step 4: Next, CQ and CP are the tangents to circle drawn from point C
∴ CQ = CP
∴ CP = CQ = QC = 7 cm (QC = 7 cm – calculated above in step 3)
Step 5: Next, from the diagram, we can see that BC = BP + PC
here BP = 3 cm (calculated above in step 1)
and PC = CP = 7 cm (calculated above in step 4)
∴ BC = 3 + 7 = 10 cm
Therefore, the length of BC is 10 cm
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