Question
Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 6 cm respectively, as shown in the figure. If AP = 6 cm then find the length of BP.
Answer: Option A
:
A
We have
OA ⊥ AP and OB ⊥ BP [ The tangent at any point of a circle is perpendicular to the radius through the point of contact].
Join OP.
In right Δ OAP, we have
OA = 8 cm, AP = 6cm
∴OP2=OA2+AP2 [by Pythagorastheorem]
⇒OP=√OA2+AP2=√82+62cm=√100cm=10cm
In right Δ OBP, we have
OB = 6cm, OP = 10cm
∴OP2=OB2+BP2
[by Pythagoras' theorem]
⇒BP=√OP2−OB2=√102−62cm=√64cm
Thus, the length of BP
=√64cm = 8cm.
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:
A
We have
OA ⊥ AP and OB ⊥ BP [ The tangent at any point of a circle is perpendicular to the radius through the point of contact].
Join OP.
In right Δ OAP, we have
OA = 8 cm, AP = 6cm
∴OP2=OA2+AP2 [by Pythagorastheorem]
⇒OP=√OA2+AP2=√82+62cm=√100cm=10cm
In right Δ OBP, we have
OB = 6cm, OP = 10cm
∴OP2=OB2+BP2
[by Pythagoras' theorem]
⇒BP=√OP2−OB2=√102−62cm=√64cm
Thus, the length of BP
=√64cm = 8cm.
Was this answer helpful ?
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