Question

In triangle ABC, AH is extended to cut the circumcircle at D where H is the orthocentre. If BH = 4 units and CD = 3 units, then CH equals

• A. 3 units
• B. 4 units
• C. 5 units
• D. data insufficient

Answer 1

Answer: (B)

4 units

As $D\perp BC$ and Bisects $BC$ equally

thus, $BD=3$

from $△BHD$ and $△CHD$

$DH=DH$ (common)

$\therefore BD=DC$

$DH=\sqrt{7}$

$CH=\sqrt{9+7}$

$CH=\sqrt{16}=4units$