Question

Two concentric circles have centre at O. op=4cm, ob=5cm,,AB is a chord of outer circle and a tangent to the inner circle at P. Find the length of AB

hey frnds pls solve this with proper steps and diagram

will be marking the correct ans as brainliest

Answer 1

Answer: AB=6cm

Step-by-step explanation:

• Refer to the figure and see ΔOAP.
• OA=OB=5cm   [∵Radius of the same circle]
• OP=4cm  [Given]
• And ∠OPA=90°      [∵AB is the tangent to the circle.]
• So,in right angled ΔOAP

        $OA^{2}=OP^{2}+PA^{2}$

    ⇒$PA^{2}=5^{2}-4^{2}$

    ⇒PA=$\sqrt{25-16}$

    ⇒PA=$\sqrt{9}$

    ∴ PA=3cm

• We know that an perpendicular drawn from the centre of circle to the chord bisects the chord.
• So,length of AB will be twice of PA.
• Length of chord AB=2×3cm

                                          =6cm

• Hence,length of chord AB is 6cm.

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