Question

In the given figure radius of the circle is 5 cm. Chords AB

and CD are parallel and distance between them is 7 cm. If

CD = 6 cm, then find AB.
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Answer 1

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Answer 2

Given that,

Radius OC = OA = 5 cm

Distance between AB and CD = 7 cm

If CD = 6 cm

If AB║CD

We need to calculate the value of CQ

Using formula for CQ

$CQ=\dfrac{1}{2}CD$

Put the value in to the formula

$CQ=\dfrac{1}{2}\times6$

$CQ=3\ cm$

We need to calculate the value of OQ

Using pythagorean theorem

$(OC)^2=(CQ)^2+(OQ)^2$

$5^2=3^2+(OQ)^2$

$25=9+(OQ)^2$

$OQ=\sqrt{25-9}$

$OQ=4\ cm$

We need to calculate the value of PO

Using formula for PO

$PO=PQ-OQ$

Put the value into the formula

$PO=(7-4)$

$PO = 3 cm$

We need to calculate the value of AP

Using pythagorean theorem

$(AP)^2=(OA)^2-(OP)^2$

Put the value into the formula

$(AP)^2=5^2-3^2$

$AP=\sqrt{25-9}$

$AP=4\ cm$

We need to calculate the value of AB

Using diagram

$AB=2AP$

Put the value in to the formula

$AB=2\times4$

$AB=8\ cm$

Hence, The value of AB is 8 cm.