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Question

From an external point $ P$, two tangents, $ PA$ and $ PB$ are drawn to a circle with centre $ O$. At one point $ E$ on the circle tangent is drawn which intersects $ PA$ and $ PB$ at $ C$ and $ D$, respectively. If $ PA=10 \mathrm{cm}$, find the perimeter of $ △PCD$

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Solution

Step 1: Given

According to the given details

From an external point P, two tangents, PA and PB are drawn to a circle with center O.

At a point E on the circle, tangent is drawn which intersects PA and PB at C and D, respectively and PA=10cm

Step 2: Determine perimeter of PCD

We know that Tangents drawn from an external point to a circle are equal.

AC=CE [Tangents from point C]

ED=DB [Tangents from point D]

Perimeter of PCD=PC+CD+PD

=PC+CE+ED+DP=PC+AC+DB+DPCE=AC,ED=DB=PA+PB=10+10PA=PB=10cm=20cm

Therefore, perimeter of PCD=20cm


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