Find AD, BF and CF in the figure.

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Solution

Tangents draw from an external point to a circle are equal

$\begin{matrix} \Rightarrow A D = A F, B D = B E, C E = C F . L e t A D = A F = a B D = B E = b C E = C F = c A B = A D + D B = a + b = 8....... (1) B C = B E + E C = b + c = 10....... (2) A C = A F + F C = a + b = 12....... (3) A d d i n g (1), (2), a n d (3), w e g e t 2 (a + b + c) = 30 \Rightarrow (a + b + c) = 15...... (4) S u b t r a c t i n g (1) f r o m (4), w e g e t c = 7 S u b t r a c t i n g (2) f r o m (4), w e g e t a = 5 S u b t r a c t i n g (3) f r o m (4), w e g e t b = 3 T h e r e f o r e, A D = a = 5 c m, B E = b = 3 c m, C F = c = 7 c m \end{matrix}$

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In the given figure, ABCD is parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

A B C D

A E ⊥ D C

C F ⊥ A D

A B = 16 c m, A E = 8 c m

C F = 10 c m

A D

A E ⊥ D C

C F ⊥ A D

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