Question
Download Solution PDFIn Δ ABC = ∠A = 2∠B. The bisector of ∠A meets BC at D such that CD = 4 cm and BD = 6 cm. The length of side AC is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
ΔABC, ∠A = 2∠B
AD bisects ∠A
CD = 4 cm
BD = 6 cm
Image of triangle ABC
Formula used:
Congruent triangles: Corresponding sides and angles are equal.
Calculation:
DC = 4 cm
BC = 6 + 4 = 10 CM
Now in Δ ACB and Δ DCA
ΔACB, ∠A = 2∠B = 2X
∠BAC = 2X, ∠ABC = X
And, Now in Δ DCB
∠ADC = 2X (Sum of interior angle is equal to opposite exterior angle.)
∠DAC = X (As AD is bisector of ∠A)
And AC is common in both the triangle.
Then by ASA(angle side angle) Δ ACB and Δ DCA is congruent.
Then,
AC/DC = CB/CA
AC2 = DC × CB
AC2 = 4 × 10
AC = 2√10
∴ The length of side AC is 2√10 cm.
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